Pub Date : 2026-01-28DOI: 10.1016/j.physd.2026.135134
K. Ferguson , B.J. Colombi , K.M. Church , O.B. Shende , Y. Zhou , J.W. Jacobs
Experiments and simulations of the Richtmyer-Meshkov instability (RMI) in two- and three-layer configurations are presented. The two-layer case utilizes a light-over-heavy configuration and consists of air as the light gas and sulfur hexafluoride (SF6) as the heavy gas. The three-layer case utilizes a light-intermediate-heavy configuration, with helium (He) as the light gas, air as the intermediate gas, and SF6 as the heavy gas. Statistically significant differences in the mixing layer width of the lower interface are not observed between the two cases. This differs from the experiments of Schalles et al. [1], where a small, though statistically significant, difference in mixing layer growth was observed between the two- and three-layer cases with a nominally two-dimensional, single mode perturbation. Notably, the perturbations on the lower interface in the present work do not grow large enough to significantly interact with the upper interface during the duration of the experiments. This suggests that the differences in mixing layer growth observed by Schalles et al. [1] may be due to interactions of the perturbations on one interface with the other interface rather than being inherent to the three-layer problem.
{"title":"Experiments and simulations on the Richtmyer-Meshkov instability with a thin intermediate layer","authors":"K. Ferguson , B.J. Colombi , K.M. Church , O.B. Shende , Y. Zhou , J.W. Jacobs","doi":"10.1016/j.physd.2026.135134","DOIUrl":"10.1016/j.physd.2026.135134","url":null,"abstract":"<div><div>Experiments and simulations of the Richtmyer-Meshkov instability (RMI) in two- and three-layer configurations are presented. The two-layer case utilizes a light-over-heavy configuration and consists of air as the light gas and sulfur hexafluoride (SF<sub>6</sub>) as the heavy gas. The three-layer case utilizes a light-intermediate-heavy configuration, with helium (He) as the light gas, air as the intermediate gas, and SF<sub>6</sub> as the heavy gas. Statistically significant differences in the mixing layer width of the lower interface are not observed between the two cases. This differs from the experiments of Schalles et al. [1], where a small, though statistically significant, difference in mixing layer growth was observed between the two- and three-layer cases with a nominally two-dimensional, single mode perturbation. Notably, the perturbations on the lower interface in the present work do not grow large enough to significantly interact with the upper interface during the duration of the experiments. This suggests that the differences in mixing layer growth observed by Schalles et al. <span><span>[1]</span></span> may be due to interactions of the perturbations on one interface with the other interface rather than being inherent to the three-layer problem.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135134"},"PeriodicalIF":2.9,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-24DOI: 10.1016/j.physd.2026.135122
Han-Lin Liao, Guo-Cheng Wu, Dong Li
Fractional differential equations frequently arise in long-range interaction processes. The center manifold theorem is an essential tool in reduction of dynamical systems. First, this paper provides existence conditions for center manifolds by constructing function spaces and fixed-point mappings. Then, determining the center manifolds becomes a parameter estimation problem. Because the chain rule for fractional derivatives cannot be applied, a neural network method is developed to find approximate center manifolds near the zero equilibrium. The automatic model selection is employed to search for a neural network architecture. Two examples are presented to demonstrate the efficiency of reducing high-dimensional fractional order systems under weak data.
{"title":"Center manifold theorem of fractional differential equations and machine learning under weak data","authors":"Han-Lin Liao, Guo-Cheng Wu, Dong Li","doi":"10.1016/j.physd.2026.135122","DOIUrl":"10.1016/j.physd.2026.135122","url":null,"abstract":"<div><div>Fractional differential equations frequently arise in long-range interaction processes. The center manifold theorem is an essential tool in reduction of dynamical systems. First, this paper provides existence conditions for center manifolds by constructing function spaces and fixed-point mappings. Then, determining the center manifolds becomes a parameter estimation problem. Because the chain rule for fractional derivatives cannot be applied, a neural network method is developed to find approximate center manifolds near the zero equilibrium. The automatic model selection is employed to search for a neural network architecture. Two examples are presented to demonstrate the efficiency of reducing high-dimensional fractional order systems under weak data.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135122"},"PeriodicalIF":2.9,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-24DOI: 10.1016/j.physd.2026.135125
Weisheng Kong, Lijuan Guo
In this paper the formation of the closed rogue patterns in the Davey-Stewartson I equation is investigated. Only one part of these wave structures in the closed rogue waves rises from the constant background and then retreats back to it, and this transient wave possesses patterns such as one ring, doubled ring, one ground and their superposition. But the other part of the wave structure comes from the far distance as some localized lumps, which moves to the near field and interacts with the closed curved waves, and then travels to the large distance again. The closed rogue patterns are determined by the roots of a special polynomial, and the number of lumps at large time could be illustrated by Young diagram. The exact and approximate results show excellent agreement. In addition, we propose that a sufficient and necessary condition to the existence of the closed rogue pattern, namely, it requires and the positive definiteness of a generalized Hermite polynomial.
{"title":"Dynamics of closed rogue patterns in the Davey-Stewartson I equation","authors":"Weisheng Kong, Lijuan Guo","doi":"10.1016/j.physd.2026.135125","DOIUrl":"10.1016/j.physd.2026.135125","url":null,"abstract":"<div><div>In this paper the formation of the closed rogue patterns in the Davey-Stewartson I equation is investigated. Only one part of these wave structures in the closed rogue waves rises from the constant background and then retreats back to it, and this transient wave possesses patterns such as one ring, doubled ring, one ground and their superposition. But the other part of the wave structure comes from the far distance as some localized lumps, which moves to the near field and interacts with the closed curved waves, and then travels to the large distance again. The closed rogue patterns are determined by the roots of a <em>special</em> polynomial, and the number of lumps at large time could be illustrated by Young diagram. The exact and approximate results show excellent agreement. In addition, we propose that a sufficient and necessary condition to the existence of the closed rogue pattern, namely, it requires <span><math><mrow><msub><mi>core</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow><mo>=</mo><mi>⌀</mi></mrow></math></span> and the positive definiteness of a generalized Hermite polynomial.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135125"},"PeriodicalIF":2.9,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.physd.2026.135116
Fernando F․ Grinstein, Vincent P․ Chiravalle, Robert K. Greene
We focus on coarse graining simulations based on the primary conservation equations, effectively codesigned physics and algorithms, and low-Mach-number corrected (LMC) hydrodynamics. Simulation methods involve LANL’s x-Radiation-Adaptive-Grid-Eulerian Large-Eddy Simulation, Besnard-Harlow-Rauenzahn (BHR) Reynolds-Averaged Navier-Stokes (RANS) approach, and Dynamic BHR – a paradigm bridging RANS and LES.
A relevant question addressed relates to whether 3D RANS and RANS/LES hybrids – the industry standards for aerospace and automotive research, are presently relevant for practical variable-density applications involving shocked and accelerated interface instabilities. Recent simulations of the GaTECH inclined mixing-layer shock-tube and NIF ICF-capsule experiments are used to demonstrate issues, challenges, and potential for 3D coarse grained LMC simulation strategies for robustly simulating complex transitional and coupled hydrodynamics-multiphysics with coarser resolution. Present LES readiness to provide accurate predictions at scale is demonstrated – whereas 3D RANS and RANS/LES bridging do not appear impactful in this context.
{"title":"Recent progress on coarse graining simulations","authors":"Fernando F․ Grinstein, Vincent P․ Chiravalle, Robert K. Greene","doi":"10.1016/j.physd.2026.135116","DOIUrl":"10.1016/j.physd.2026.135116","url":null,"abstract":"<div><div>We focus on coarse graining simulations based on the primary conservation equations, effectively codesigned physics and algorithms, and low-Mach-number corrected (LMC) hydrodynamics. Simulation methods involve LANL’s x-Radiation-Adaptive-Grid-Eulerian Large-Eddy Simulation, Besnard-Harlow-Rauenzahn (BHR) Reynolds-Averaged Navier-Stokes (RANS) approach, and Dynamic BHR – a paradigm bridging RANS and LES.</div><div><em>A relevant question addressed relates to whether 3D RANS and RANS/LES hybrids – the industry standards for aerospace and automotive research, are presently relevant for practical variable-density applications involving shocked and accelerated interface instabilities</em>. Recent simulations of the GaTECH inclined mixing-layer shock-tube and NIF ICF-capsule experiments are used to demonstrate issues, challenges, and potential for 3D coarse grained LMC simulation strategies for robustly simulating complex transitional and coupled hydrodynamics-multiphysics with coarser resolution. <em>Present LES readiness to provide accurate predictions at scale is demonstrated – whereas 3D RANS and RANS/LES bridging do not appear impactful in this context.</em></div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135116"},"PeriodicalIF":2.9,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.physd.2026.135123
Nikos I. Karachalios , Dionyssios Mantzavinos , Jeffrey Oregero
The distance between the solutions to the integrable Korteweg-de Vries (KdV) equation and a broad class of non-integrable generalized KdV (gKdV) equations is estimated in appropriate Sobolev spaces. This family of equations includes, as special cases, the standard gKdV equation with power nonlinearities as well as weakly nonlinear perturbations of the KdV equation. For initial data and nonlinearity parameters of arbitrary size, we establish distance estimates based on a crucial size estimate for local gKdV solutions that grows linearly with the norm of the initial data. Consequently, these estimates predict that the dynamics of the gKdV and KdV equations remain close over long time intervals for initial amplitudes approaching unity, while providing an explicit rate of deviation for larger amplitudes. These theoretical results are supported by numerical simulations of one-soliton and two-soliton initial conditions, which show excellent agreement with the theoretical predictions. Furthermore, it is demonstrated that in the case of power nonlinearities and large solitonic initial data, the deviation between the integrable and non-integrable dynamics can be drastically reduced by incorporating suitable rotation effects via a rescaled KdV equation. As a result, the integrable dynamics stemming from the rescaled KdV equation may persist within the gKdV family of equations over remarkably long timescales.
{"title":"On the proximal dynamics between integrable and non-integrable members of a generalized Korteweg-de Vries family of equations","authors":"Nikos I. Karachalios , Dionyssios Mantzavinos , Jeffrey Oregero","doi":"10.1016/j.physd.2026.135123","DOIUrl":"10.1016/j.physd.2026.135123","url":null,"abstract":"<div><div>The distance between the solutions to the integrable Korteweg-de Vries (KdV) equation and a broad class of non-integrable generalized KdV (gKdV) equations is estimated in appropriate Sobolev spaces. This family of equations includes, as special cases, the standard gKdV equation with power nonlinearities as well as weakly nonlinear perturbations of the KdV equation. For initial data and nonlinearity parameters of arbitrary size, we establish distance estimates based on a crucial size estimate for local gKdV solutions that grows linearly with the norm of the initial data. Consequently, these estimates predict that the dynamics of the gKdV and KdV equations remain close over long time intervals for initial amplitudes approaching unity, while providing an explicit rate of deviation for larger amplitudes. These theoretical results are supported by numerical simulations of one-soliton and two-soliton initial conditions, which show excellent agreement with the theoretical predictions. Furthermore, it is demonstrated that in the case of power nonlinearities and large solitonic initial data, the deviation between the integrable and non-integrable dynamics can be drastically reduced by incorporating suitable rotation effects via a rescaled KdV equation. As a result, the integrable dynamics stemming from the rescaled KdV equation may persist within the gKdV family of equations over remarkably long timescales.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135123"},"PeriodicalIF":2.9,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.physd.2026.135121
Wennan Zou, Jian He
The contact structures of fluid are described by the streamline pattern in steady flows, where the key to determine the slip topology the streamline pattern around the isotropic point, called the local streamline pattern (LSP). In this paper, taking homogeneous quadratic velocity fields (HQVFs) as the research object and utilizing the swirl field, which is an axis-vector-valued differential 1-form determined by the velocity direction, to define the topological degree, we establish an analytical framework for three-dimensional nonlinear velocity fields. After obtaining the trivial result of the topological degree of three-dimensional HQVFs, we make use of the characteristic problems of high order tensor to work out all radial streamlines entering/exiting an isotropic point, and adopt the pair number of radial streamlines as the key criterion to classify the LSPs. Some typical HQVFs are illustrated for discussion, and the investigation on linear velocity fields shows their particularity. As a preliminary exploration of the streamline pattern of three-dimensional nonlinear velocity fields, this work demonstrates how difficult it is to generalize the research results of two-dimensional velocity fields and three-dimensional linear velocity fields.
{"title":"Slip topology of three-dimensional homogeneous quadratic velocity fields","authors":"Wennan Zou, Jian He","doi":"10.1016/j.physd.2026.135121","DOIUrl":"10.1016/j.physd.2026.135121","url":null,"abstract":"<div><div>The contact structures of fluid are described by the streamline pattern in steady flows, where the key to determine the slip topology the streamline pattern around the isotropic point, called the local streamline pattern (LSP). In this paper, taking homogeneous quadratic velocity fields (HQVFs) as the research object and utilizing the swirl field, which is an axis-vector-valued differential 1-form determined by the velocity direction, to define the topological degree, we establish an analytical framework for three-dimensional nonlinear velocity fields. After obtaining the trivial result of the topological degree of three-dimensional HQVFs, we make use of the characteristic problems of high order tensor to work out all radial streamlines entering/exiting an isotropic point, and adopt the pair number of radial streamlines as the key criterion to classify the LSPs. Some typical HQVFs are illustrated for discussion, and the investigation on linear velocity fields shows their particularity. As a preliminary exploration of the streamline pattern of three-dimensional nonlinear velocity fields, this work demonstrates how difficult it is to generalize the research results of two-dimensional velocity fields and three-dimensional linear velocity fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135121"},"PeriodicalIF":2.9,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-18DOI: 10.1016/j.physd.2026.135119
Edoardo Peroni , Jing Ping Wang
We construct linear and quadratic Darboux matrices compatible with the reduction group of the Lax operator for each of the seven known non-Abelian derivative nonlinear Schrödinger equations that admit Lax representations. The differential-difference systems derived from these Darboux transformations generalise established non-Abelian integrable models by incorporating non-commutative constants. Specifically, we demonstrate that linear Darboux transformations generate non-Abelian Volterra-type equations, while quadratic transformations yield two-component systems, including non-Abelian versions of the Ablowitz-Ladik, Merola-Ragnisco-Tu, and relativistic Toda equations. Using quasideterminants, we establish necessary conditions for factorising a higher-degree polynomial Darboux matrix with a specific linear Darboux matrix as a factor. This result enables the factorisation of quadratic Darboux matrices into pairs of linear Darboux matrices.
{"title":"Darboux transformations and related non-Abelian integrable differential-difference systems of the derivative nonlinear Schrödinger type","authors":"Edoardo Peroni , Jing Ping Wang","doi":"10.1016/j.physd.2026.135119","DOIUrl":"10.1016/j.physd.2026.135119","url":null,"abstract":"<div><div>We construct linear and quadratic Darboux matrices compatible with the reduction group of the Lax operator for each of the seven known non-Abelian derivative nonlinear Schrödinger equations that admit Lax representations. The differential-difference systems derived from these Darboux transformations generalise established non-Abelian integrable models by incorporating non-commutative constants. Specifically, we demonstrate that linear Darboux transformations generate non-Abelian Volterra-type equations, while quadratic transformations yield two-component systems, including non-Abelian versions of the Ablowitz-Ladik, Merola-Ragnisco-Tu, and relativistic Toda equations. Using quasideterminants, we establish necessary conditions for factorising a higher-degree polynomial Darboux matrix with a specific linear Darboux matrix as a factor. This result enables the factorisation of quadratic Darboux matrices into pairs of linear Darboux matrices.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135119"},"PeriodicalIF":2.9,"publicationDate":"2026-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-17DOI: 10.1016/j.physd.2026.135120
Yonghui Zhou , Xiaowan Li , Shuguan Ji , Zhijun Qiao
In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato’s theorem. Then we give the necessary and sufficient condition for the occurrence of wave breaking in a finite time. Finally, we investigate the persistence properties of strong solutions in the weighted spaces for a large class of moderate weights.
{"title":"A generalized two-component Novikov system and its analytical properties","authors":"Yonghui Zhou , Xiaowan Li , Shuguan Ji , Zhijun Qiao","doi":"10.1016/j.physd.2026.135120","DOIUrl":"10.1016/j.physd.2026.135120","url":null,"abstract":"<div><div>In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato’s theorem. Then we give the necessary and sufficient condition for the occurrence of wave breaking in a finite time. Finally, we investigate the persistence properties of strong solutions in the weighted <span><math><mrow><msup><mi>L</mi><mi>p</mi></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> spaces for a large class of moderate weights.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135120"},"PeriodicalIF":2.9,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.1016/j.physd.2026.135118
Oleg Schilling
A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D 402, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter θm, and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, θmol. The scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. The explicit modeling and solution of turbulent transport equations are not required. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.
{"title":"A buoyancy–shear–drag–scalar-based turbulence model for power-law acceleration-driven Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing","authors":"Oleg Schilling","doi":"10.1016/j.physd.2026.135118","DOIUrl":"10.1016/j.physd.2026.135118","url":null,"abstract":"<div><div>A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D <strong>402</strong>, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter <em>θ<sub>m</sub></em>, and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, <em>θ<sub>mol</sub></em>. The scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. <em>The explicit modeling and solution of turbulent transport equations are not required</em>. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"489 ","pages":"Article 135118"},"PeriodicalIF":2.9,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.1016/j.physd.2026.135117
Yufeng Liu , Jin Song , Zhenya Yan
In this paper, we investigate the dynamical behaviors of soliton solutions and rogue waves in Bose-Einstein condensates, modelled by the focusing and defocusing Gross-Pitaevskii equations. Our work uniquely integrates the effects of a density-dependent gauge potential with two novel types of parity-time () symmetric potentials: the generalized -symmetric harmonic-Gaussian potential and the generalized -symmetric Scarf-II potential. This specific combination provides a rich platform for exploring the phenomenon of matter waves. Firstly, we analyze the linear spectral problem to determine the entirely real spectral region of the non-Hermitian Hamiltonian and examine the occurrence of the phase-breaking phenomena. Then, we discuss the exact solutions for both types of -symmetric external potentials, as well as the numerical solutions for the ground state and dipole modes, while analyzing their stability using the corresponding Bogoliubov-de Gennes equations. Moreover, we investigate the effect of the current nonlinearity on the stability of exact solitons. In particular, the interactions between two solitons are studied, exhibiting nearly elastic and inelastic interactions. Furthermore, the stable adiabatic excitations of solitons are investigated. Finally, due to the influence of current nonlinearity on its structure, the high-order rogue wave generated by several Gaussian perturbations on the continuous wave undergoes a transformation into chiral solitons with lower amplitude. Our research provides in-depth insights into the dynamic behavior of solitons and rogue waves in novel systems with density-dependent gauge potential and -symmetric external potential, offering important guidance for future theoretical research and experimental exploration of complex matter wave phenomena.
{"title":"Bose-Einstein condensates with density-dependent gauge potential and two PT-symmetric potentials: Solitons, rogue waves and nonlinear dynamics","authors":"Yufeng Liu , Jin Song , Zhenya Yan","doi":"10.1016/j.physd.2026.135117","DOIUrl":"10.1016/j.physd.2026.135117","url":null,"abstract":"<div><div>In this paper, we investigate the dynamical behaviors of soliton solutions and rogue waves in Bose-Einstein condensates, modelled by the focusing and defocusing Gross-Pitaevskii equations. Our work uniquely integrates the effects of a density-dependent gauge potential with two novel types of parity-time (<span><math><mi>PT</mi></math></span>) symmetric potentials: the generalized <span><math><mi>PT</mi></math></span>-symmetric harmonic-Gaussian potential and the generalized <span><math><mi>PT</mi></math></span>-symmetric Scarf-II potential. This specific combination provides a rich platform for exploring the phenomenon of matter waves. Firstly, we analyze the linear spectral problem to determine the entirely real spectral region of the non-Hermitian Hamiltonian and examine the occurrence of the phase-breaking phenomena. Then, we discuss the exact solutions for both types of <span><math><mi>PT</mi></math></span>-symmetric external potentials, as well as the numerical solutions for the ground state and dipole modes, while analyzing their stability using the corresponding Bogoliubov-de Gennes equations. Moreover, we investigate the effect of the current nonlinearity on the stability of exact solitons. In particular, the interactions between two solitons are studied, exhibiting nearly elastic and inelastic interactions. Furthermore, the stable adiabatic excitations of solitons are investigated. Finally, due to the influence of current nonlinearity on its structure, the high-order rogue wave generated by several Gaussian perturbations on the continuous wave undergoes a transformation into chiral solitons with lower amplitude. Our research provides in-depth insights into the dynamic behavior of solitons and rogue waves in novel systems with density-dependent gauge potential and <span><math><mi>PT</mi></math></span>-symmetric external potential, offering important guidance for future theoretical research and experimental exploration of complex matter wave phenomena.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135117"},"PeriodicalIF":2.9,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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