In this paper, we study the stationary solutions of the inflow problem for a compressible model of the viscous ions motion, which is given by the one-dimensional isentropic compressible Navier–Stokes–Poisson equations. The unique existence of the stationary solutions to the one-dimensional isentropic compressible Navier–Stokes–Poisson equations in the half line is shown provided that the boundary data satisfy some smallness conditions. Moreover, the spatial decay rates of the stationary solutions are presented. By taking the accurate analysis of the cubic characteristic equation for the linearized stationary system, the sign of the real part corresponding to the eigenvalues can be sure. Then our results can be proven by the manifold theory and the center manifold theorem.
{"title":"Stationary Solutions to an Inflow Problem for a Compressible Model of the Viscous Ions Motion","authors":"Yeping Li, Qiwei Wu","doi":"10.1111/sapm.70121","DOIUrl":"https://doi.org/10.1111/sapm.70121","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study the stationary solutions of the inflow problem for a compressible model of the viscous ions motion, which is given by the one-dimensional isentropic compressible Navier–Stokes–Poisson equations. The unique existence of the stationary solutions to the one-dimensional isentropic compressible Navier–Stokes–Poisson equations in the half line is shown provided that the boundary data satisfy some smallness conditions. Moreover, the spatial decay rates of the stationary solutions are presented. By taking the accurate analysis of the cubic characteristic equation for the linearized stationary system, the sign of the real part corresponding to the eigenvalues can be sure. Then our results can be proven by the manifold theory and the center manifold theorem.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by previous results in special cases associated with Ricci flows, all possible two-components evolutions systems of (1+2)-dimensional second-order partial differential equations (PDEs) admitting an infinite-dimensional Lie algebra are constructed. It is shown that a natural generalization of this Lie algebra to the higher-dimensional case does not lead to a more general result because the infinite-dimensional symmetry is broken. The recently derived system, which is related to Ricci flows, is identified as a very particular case among the evolution systems obtained. All possible radially symmetric stationary solutions of the Ricci-flow-associated special case are then constructed using the surprisingly rich Lie algebra of the resulting reduced system of ordinary differential equations (ODEs), exemplifying the exceptional status of such systems. Moreover, it is proved that this Lie algebra is reducible to the fifteen-dimensional algebra of the simplest system of two second-order ODEs. Several time-dependent exact solutions in the radially symmetric case are constructed as well. It is shown that the solutions obtained are bounded and smooth provided arbitrary parameters are correctly specified. By their nature, geometric PDEs typically enjoy rich symmetry properties; our analysis illustrates how those properties may be extrapolated to broader classes of models that are of independent interest.
{"title":"Nonlinear Systems of PDEs Admitting Infinite-Dimensional Lie Algebras and Their Connection With Ricci Flows. II: The Two-Dimensional Space Case","authors":"Roman Cherniha, John R. King","doi":"10.1111/sapm.70120","DOIUrl":"https://doi.org/10.1111/sapm.70120","url":null,"abstract":"<p>Motivated by previous results in special cases associated with Ricci flows, all possible two-components evolutions systems of (1+2)-dimensional second-order partial differential equations (PDEs) admitting an infinite-dimensional Lie algebra are constructed. It is shown that a natural generalization of this Lie algebra to the higher-dimensional case does not lead to a more general result because the infinite-dimensional symmetry is broken. The recently derived system, which is related to Ricci flows, is identified as a very particular case among the evolution systems obtained. All possible radially symmetric stationary solutions of the Ricci-flow-associated special case are then constructed using the surprisingly rich Lie algebra of the resulting reduced system of ordinary differential equations (ODEs), exemplifying the exceptional status of such systems. Moreover, it is proved that this Lie algebra is reducible to the fifteen-dimensional algebra of the simplest system of two second-order ODEs. Several time-dependent exact solutions in the radially symmetric case are constructed as well. It is shown that the solutions obtained are bounded and smooth provided arbitrary parameters are correctly specified. By their nature, geometric PDEs typically enjoy rich symmetry properties; our analysis illustrates how those properties may be extrapolated to broader classes of models that are of independent interest.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70120","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the spatiotemporal dynamics of a single-species diffusive model incorporating maturation delay in closed advective heterogeneous environments. First, we establish the well-posedness of the system and prove the existence and uniqueness of the nonconstant positive steady state. Subsequently, we analyze the local stability of the unique nonconstant positive steady state and demonstrate the occurrence of Hopf bifurcation through the corresponding eigenvalue problem. By utilizing a weighted inner product parameterized by the advection rate, we further characterize the stability and direction of the Hopf bifurcation. Finally, we examine how advection rate and spatial length influence the first Hopf bifurcation value, revealing their effects on system dynamics. Our results demonstrate that both advection and spatial scale can either enhance or suppress the likelihood of Hopf bifurcation, depending on the spatial heterogeneity of the intrinsic growth rate.
{"title":"Spatiotemporal Dynamics of a Delayed Diffusive Single-Species Model in Closed Advective Environments","authors":"Shixia Xin, Hongying Shu, Hua Nie","doi":"10.1111/sapm.70122","DOIUrl":"https://doi.org/10.1111/sapm.70122","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate the spatiotemporal dynamics of a single-species diffusive model incorporating maturation delay in closed advective heterogeneous environments. First, we establish the well-posedness of the system and prove the existence and uniqueness of the nonconstant positive steady state. Subsequently, we analyze the local stability of the unique nonconstant positive steady state and demonstrate the occurrence of Hopf bifurcation through the corresponding eigenvalue problem. By utilizing a weighted inner product parameterized by the advection rate, we further characterize the stability and direction of the Hopf bifurcation. Finally, we examine how advection rate and spatial length influence the first Hopf bifurcation value, revealing their effects on system dynamics. Our results demonstrate that both advection and spatial scale can either enhance or suppress the likelihood of Hopf bifurcation, depending on the spatial heterogeneity of the intrinsic growth rate.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145196467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In nonisothermal setting, microstructural interactions may determine finite-speed heat propagation. We consider such an effect in the dynamics of a viscous incompressible complex fluid (i.e., one with “active” microstructure) through a porous medium. Nonlocal actions and nonlinear damping are considered as determined by the solid–fluid and microstructural interactions. After a choice of constitutive structures and the introduction of a specific truncation of some higher-order terms, we prove existence and uniqueness of global strong solutions to the balance equations. We also analyze pertinent weak solutions.
{"title":"Microstructure-Induced Finite-Speed Heat Propagation in Fluids Through Porous Media: Analytical Results","authors":"Luca Bisconti, Paolo Maria Mariano","doi":"10.1111/sapm.70118","DOIUrl":"https://doi.org/10.1111/sapm.70118","url":null,"abstract":"<p>In nonisothermal setting, microstructural interactions may determine finite-speed heat propagation. We consider such an effect in the dynamics of a viscous incompressible complex fluid (i.e., one with “active” microstructure) through a porous medium. Nonlocal actions and nonlinear damping are considered as determined by the solid–fluid and microstructural interactions. After a choice of constitutive structures and the introduction of a specific truncation of some higher-order terms, we prove existence and uniqueness of global strong solutions to the balance equations. We also analyze pertinent weak solutions.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70118","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145196469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales that are exponentially long with respect to the noise strength. This is achieved by means of a stochastic phase-tracking mechanism that can be maintained over such long timescales. The corresponding mild formulation of our problem features stochastic integrals with respect to anticipating integrands, which hence cannot be understood within the well-established setting of Itô-integrals. To circumvent this problem, we exploit and extend recently developed theory concerning forward integrals.
{"title":"Multidimensional Stability of Planar Traveling Waves for Stochastically Perturbed Reaction–Diffusion Systems","authors":"M. van den Bosch, H. J. Hupkes","doi":"10.1111/sapm.70114","DOIUrl":"https://doi.org/10.1111/sapm.70114","url":null,"abstract":"<p>We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales that are exponentially long with respect to the noise strength. This is achieved by means of a stochastic phase-tracking mechanism that can be maintained over such long timescales. The corresponding mild formulation of our problem features stochastic integrals with respect to anticipating integrands, which hence cannot be understood within the well-established setting of Itô-integrals. To circumvent this problem, we exploit and extend recently developed theory concerning forward integrals.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70114","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145146415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Annachiara Colombi, Andrea Battaglia, Chiara Giverso
Experiments have shown that mechanical cues play a central role in determining the direction and rate of axonal growth. In particular, neurons seeded on planar substrates undergoing periodic stretching have been shown to reorient and reach a stable equilibrium orientation corresponding to angles within the interval with respect to the main stretching direction. In this work, we present a new model that considers both the reorientation and growth of neurons in response to cyclic stretching. Specifically, a linear viscoelastic model for the growth cone reorientation with the addition of a stochastic term is merged with a moving-boundary model for tubulin-driven neurite growth to simulate the axonal pathfinding process. Various combinations of stretching frequencies and strain amplitudes have been tested by numerical simulation of the proposed model. The simulations show that neurons tend to reorient toward an equilibrium angle that falls in the experimentally observed range. Moreover, the model captures the relation between the stretching condition and the speed of reorientation. Indeed, numerical results show that neurons tend to reorient faster as the frequency and amplitude of oscillation increase.
{"title":"A Mathematical Model for Neuron Reorientation and Axonal Growth on a Cyclically Stretched Substrate","authors":"Annachiara Colombi, Andrea Battaglia, Chiara Giverso","doi":"10.1111/sapm.70103","DOIUrl":"https://doi.org/10.1111/sapm.70103","url":null,"abstract":"<p>Experiments have shown that mechanical cues play a central role in determining the direction and rate of axonal growth. In particular, neurons seeded on planar substrates undergoing periodic stretching have been shown to reorient and reach a stable equilibrium orientation corresponding to angles within the interval <span></span><math>\u0000 <semantics>\u0000 <mfenced>\u0000 <msup>\u0000 <mn>60</mn>\u0000 <mo>∘</mo>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mn>90</mn>\u0000 <mo>∘</mo>\u0000 </msup>\u0000 </mfenced>\u0000 <annotation>$left[60^{circ },90^{circ }right]$</annotation>\u0000 </semantics></math> with respect to the main stretching direction. In this work, we present a new model that considers both the reorientation and growth of neurons in response to cyclic stretching. Specifically, a linear viscoelastic model for the growth cone reorientation with the addition of a stochastic term is merged with a moving-boundary model for tubulin-driven neurite growth to simulate the axonal pathfinding process. Various combinations of stretching frequencies and strain amplitudes have been tested by numerical simulation of the proposed model. The simulations show that neurons tend to reorient toward an equilibrium angle that falls in the experimentally observed range. Moreover, the model captures the relation between the stretching condition and the speed of reorientation. Indeed, numerical results show that neurons tend to reorient faster as the frequency and amplitude of oscillation increase.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145146311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Denis A. Silantyev, Pavel M. Lushnikov, Michael Siegel, David M. Ambrose
<div> <p>We present exact pole dynamics solutions to the generalized Constantin–Lax–Majda (gCLM) equation in a periodic geometry with dissipation <span></span><math> <semantics> <mrow> <mo>−</mo> <msup> <mi>Λ</mi> <mi>σ</mi> </msup> </mrow> <annotation>$-Lambda ^sigma$</annotation> </semantics></math>, where its spatial Fourier transform is <span></span><math> <semantics> <mrow> <mover> <msup> <mi>Λ</mi> <mi>σ</mi> </msup> <mo>̂</mo> </mover> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mi>k</mi> <mo>|</mo> </mrow> <mi>σ</mi> </msup> </mrow> <annotation>$widehat{Lambda ^sigma }=|k|^sigma$</annotation> </semantics></math>. The gCLM equation is a simplified model for singularity formation in the 3D incompressible Euler equations. It includes an advection term with parameter <span></span><math> <semantics> <mi>a</mi> <annotation>$a$</annotation> </semantics></math>, which allows different relative weights for advection and vortex stretching. There has been intense interest in the gCLM equation, and it has served as a proving ground for the development of methods to study singularity formation in the 3D Euler equations. Several exact solutions for the problem on the real line have been previously found by the method of pole dynamics, but only one such solution has been reported for the periodic geometry. We derive new periodic solutions for <span></span><math> <semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0</mn> </mrow> <annotation>$a=0$</annotation> </semantics></math> and <span></span><math> <semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <annotation>$1/2$</annotation> </semantics></math> and <span></span><math> <semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0</mn> </mrow> <annotation>$sigma =0$</annotation> </semantics></math> and 1, for which a closed collection of (periodically repeated) poles evolve in the complex plane. Self-similar finite-time blowup of the solutions is analyzed and compared for the different values of <span></span><math>
{"title":"Exact Periodic Solutions of the Generalized Constantin–Lax–Majda Equation With Dissipation","authors":"Denis A. Silantyev, Pavel M. Lushnikov, Michael Siegel, David M. Ambrose","doi":"10.1111/sapm.70115","DOIUrl":"https://doi.org/10.1111/sapm.70115","url":null,"abstract":"<div>\u0000 \u0000 <p>We present exact pole dynamics solutions to the generalized Constantin–Lax–Majda (gCLM) equation in a periodic geometry with dissipation <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <msup>\u0000 <mi>Λ</mi>\u0000 <mi>σ</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$-Lambda ^sigma$</annotation>\u0000 </semantics></math>, where its spatial Fourier transform is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <msup>\u0000 <mi>Λ</mi>\u0000 <mi>σ</mi>\u0000 </msup>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>k</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <mi>σ</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$widehat{Lambda ^sigma }=|k|^sigma$</annotation>\u0000 </semantics></math>. The gCLM equation is a simplified model for singularity formation in the 3D incompressible Euler equations. It includes an advection term with parameter <span></span><math>\u0000 <semantics>\u0000 <mi>a</mi>\u0000 <annotation>$a$</annotation>\u0000 </semantics></math>, which allows different relative weights for advection and vortex stretching. There has been intense interest in the gCLM equation, and it has served as a proving ground for the development of methods to study singularity formation in the 3D Euler equations. Several exact solutions for the problem on the real line have been previously found by the method of pole dynamics, but only one such solution has been reported for the periodic geometry. We derive new periodic solutions for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$a=0$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$1/2$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$sigma =0$</annotation>\u0000 </semantics></math> and 1, for which a closed collection of (periodically repeated) poles evolve in the complex plane. Self-similar finite-time blowup of the solutions is analyzed and compared for the different values of <span></span><math>\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the Korteweg–de Vries (KdV) equation on the real line with an interface. Using Fokas's unified transform method, the explicit solution formulas for the linear forced KdV equation with an interface are derived. Building on these solution formulas, we establish standard estimates for the linear solution and a bilinear estimate for the nonlinear term in a suitable Sobolev space. Using these estimates and a contraction mapping argument, we prove the local well-posedness for the KdV equation with an interface.
{"title":"The Korteweg-de Vries Equation With an Interface","authors":"Hsin-Yuan Huang, Cheng-Pu Lin","doi":"10.1111/sapm.70117","DOIUrl":"https://doi.org/10.1111/sapm.70117","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider the Korteweg–de Vries (KdV) equation on the real line with an interface. Using Fokas's unified transform method, the explicit solution formulas for the linear forced KdV equation with an interface are derived. Building on these solution formulas, we establish standard estimates for the linear solution and a bilinear estimate for the nonlinear term in a suitable Sobolev space. Using these estimates and a contraction mapping argument, we prove the local well-posedness for the KdV equation with an interface.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study integrable boundary conditions for the whole hierarchy of nonlinear Schrödinger (NLS) equations defined on the half-line. We find that the even-order and odd-order NLS equations admit rather different integrable boundary conditions. In particular, the odd-order NLS equations admit a new class of integrable boundary conditions that involves time reversal. We establish the integrability of the NLS hierarchy with our new boundary conditions by demonstrating the existence of infinitely many integrals of motion in involution. Moreover, we develop the boundary dressing technique to construct soliton solutions satisfying these new boundary conditions.
{"title":"Integrable Boundary Conditions for the Nonlinear Schrödinger Hierarchy Via the Fokas Method","authors":"Baoqiang Xia","doi":"10.1111/sapm.70116","DOIUrl":"https://doi.org/10.1111/sapm.70116","url":null,"abstract":"<div>\u0000 \u0000 <p>We study integrable boundary conditions for the whole hierarchy of nonlinear Schrödinger (NLS) equations defined on the half-line. We find that the even-order and odd-order NLS equations admit rather different integrable boundary conditions. In particular, the odd-order NLS equations admit a new class of integrable boundary conditions that involves time reversal. We establish the integrability of the NLS hierarchy with our new boundary conditions by demonstrating the existence of infinitely many integrals of motion in involution. Moreover, we develop the boundary dressing technique to construct soliton solutions satisfying these new boundary conditions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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