Pub Date : 2024-10-21DOI: 10.1016/j.physd.2024.134409
Jeongho Kim , Bora Moon , Jinyeong Park
In this paper, we introduce the Vlasov–Chern–Simons (VCS) equation, a Vlasov-type equation that describes the two-dimensional dynamics of charged particles affected by the Chern–Simons electromagnetic potentials. First, we derive the VCS equation from the Chern–Simons–Schrödinger equations, a quantum mechanical model for the particle affected by Chern–Simons gauge fields, via the Wigner transform. Subsequently, we study the local-in-time well-posedness for the strong solution and the global-in-time existence for weak solutions to the VCS equation, respectively. Additionally, we propose a simple semi-Lagrangian numerical scheme for solving the VCS equation and validate the conservation of total moments and -norms through numerical tests.
{"title":"A kinetic description for the electromagnetic response of the charged particles to Chern–Simons gauge fields","authors":"Jeongho Kim , Bora Moon , Jinyeong Park","doi":"10.1016/j.physd.2024.134409","DOIUrl":"10.1016/j.physd.2024.134409","url":null,"abstract":"<div><div>In this paper, we introduce the Vlasov–Chern–Simons (VCS) equation, a Vlasov-type equation that describes the two-dimensional dynamics of charged particles affected by the Chern–Simons electromagnetic potentials. First, we derive the VCS equation from the Chern–Simons–Schrödinger equations, a quantum mechanical model for the particle affected by Chern–Simons gauge fields, via the Wigner transform. Subsequently, we study the local-in-time well-posedness for the strong solution and the global-in-time existence for weak solutions to the VCS equation, respectively. Additionally, we propose a simple semi-Lagrangian numerical scheme for solving the VCS equation and validate the conservation of total moments and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norms through numerical tests.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552586","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}
We investigate a potential model for an unbounded celestial bodies of finite mass composed of a solid core and a gaseous atmosphere. The system is governed by the Navier–Stokes–Fourier–Poisson equations, incorporating no-slip boundary conditions for velocity and a specified temperature distribution on the surface of the solid core. Additionally, a positive far-field condition is imposed on the temperature. This manuscript extends the mathematical theory of open fluid systems to unbounded exterior domains addressing these physically motivated yet highly challenging combination of boundary conditions. Notably, we establish the existence of global-in-time weak solutions and demonstrate the weak–strong uniqueness principle
{"title":"On thermally driven fluid flows arising in astrophysics","authors":"Nilasis Chaudhuri , Eduard Feireisl , Ewelina Zatorska , Bogusław Zegarliński","doi":"10.1016/j.physd.2024.134401","DOIUrl":"10.1016/j.physd.2024.134401","url":null,"abstract":"<div><div>We investigate a potential model for an unbounded celestial bodies of finite mass composed of a solid core and a gaseous atmosphere. The system is governed by the Navier–Stokes–Fourier–Poisson equations, incorporating no-slip boundary conditions for velocity and a specified temperature distribution on the surface of the solid core. Additionally, a positive far-field condition is imposed on the temperature. This manuscript extends the mathematical theory of open fluid systems to unbounded exterior domains addressing these physically motivated yet highly challenging combination of boundary conditions. Notably, we establish the existence of global-in-time weak solutions and demonstrate the weak–strong uniqueness principle</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552589","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 : 2024-10-16DOI: 10.1016/j.physd.2024.134397
N. Nikishina , E. Rybalova , A. Zakharova , G. Strelkova , T. Vadivasova
We explore numerically the complex dynamics of multilayer networks (consisting of three and one hundred layers) of cubic maps in the presence of noise-modulated interlayer coupling (multiplexing noise). The coupling strength is defined by independent discrete-time sources of color Gaussian noise. Uncoupled layers can demonstrate different complex structures, such as double-well chimeras, coherent and spatially incoherent regimes. Regions of partial synchronization of these structures are identified in the presence of multiplexing noise. We elucidate how synchronization of a three-layer network depends on the initially observed structures in the layers and construct synchronization regions in the plane of multiplexing noise parameters “noise spectrum width – noise intensity”. It is shown that in a hundred-layer network, clusters of synchronized layers can be formed at certain optimal values of multiplexing noise parameters. The performed numerical studies confidently indicate that the spatial dynamics of multilayer networks can be controlled by varying multiplexing noise parameters.
{"title":"Impact of multiplexing noise on multilayer networks of bistable maps","authors":"N. Nikishina , E. Rybalova , A. Zakharova , G. Strelkova , T. Vadivasova","doi":"10.1016/j.physd.2024.134397","DOIUrl":"10.1016/j.physd.2024.134397","url":null,"abstract":"<div><div>We explore numerically the complex dynamics of multilayer networks (consisting of three and one hundred layers) of cubic maps in the presence of noise-modulated interlayer coupling (multiplexing noise). The coupling strength is defined by independent discrete-time sources of color Gaussian noise. Uncoupled layers can demonstrate different complex structures, such as double-well chimeras, coherent and spatially incoherent regimes. Regions of partial synchronization of these structures are identified in the presence of multiplexing noise. We elucidate how synchronization of a three-layer network depends on the initially observed structures in the layers and construct synchronization regions in the plane of multiplexing noise parameters “noise spectrum width – noise intensity”. It is shown that in a hundred-layer network, clusters of synchronized layers can be formed at certain optimal values of multiplexing noise parameters. The performed numerical studies confidently indicate that the spatial dynamics of multilayer networks can be controlled by varying multiplexing noise parameters.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529720","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 : 2024-10-13DOI: 10.1016/j.physd.2024.134404
Mingpei Lin , Tong Luo , Hayato Chiba
A unified semi-analytical solution is presented for constructing the phase space near collinear libration points in the Circular Restricted Three-body Problem (CRTBP), encompassing Lissajous orbits, quasihalo orbits, Axial orbits, and their invariant manifolds, as well as transit and non-transit orbits. Based on classical in-plane and out-of-plane frequency resonance mechanisms, the Lindstedt–Poincaré method could only derive separate analytical solutions for the invariant manifolds of Lissajous orbits and halo orbits, falling short for the invariant manifolds of quasihalo orbits. In this paper, by introducing a coupling coefficient η and a bifurcation equation, a unified series solution for these orbits is systematically developed using a coupling-induced bifurcation mechanism and Lindstedt–Poincaré method. Analyzing the bifurcation equation obtained from different coupling forms reveals bifurcation conditions for all kinds of orbits near collinear libration points. When η = 0, the series solution describes non-bifurcated orbits, while when η ≠ 0, the solution describes bifurcated orbits, including quasihalo orbits, Axial orbits, and their invariant manifolds, as well as newly bifurcated transit and non-transit orbits. This unified semi-analytical framework provides a more comprehensive understanding of the complex phase space structures near collinear libration points in the CRTBP.
本文提出了一种统一的半解析解，用于构建环形受限三体问题（CRTBP）中碰撞天平点附近的相空间，包括利萨如轨道、准光轨道、轴轨道及其不变流形，以及凌日轨道和非凌日轨道。基于经典的面内和面外频率共振机制，Lindstedt-Poincaré 方法只能分别求出 Lissajous 轨道和光环轨道的不变流形的解析解，而准光环轨道的不变流形的解析解则不尽人意。本文通过引入耦合系数η和分岔方程，利用耦合诱导的分岔机制和林斯特-普因卡雷方法，系统地建立了这些轨道的统一级数解。通过分析不同耦合形式得到的分岔方程，揭示了碰撞天平点附近各种轨道的分岔条件。当 η = 0 时，序列解描述的是非分岔轨道；而当 η ≠ 0 时，解描述的是分岔轨道，包括准晕轨道、轴轨道及其不变流形，以及新分岔的过境轨道和非过境轨道。这种统一的半分析框架使我们能够更全面地理解 CRTBP 碰撞天平点附近的复杂相空间结构。
{"title":"Semi-analytical computation of bifurcation of orbits near collinear libration point in the restricted three-body problem","authors":"Mingpei Lin , Tong Luo , Hayato Chiba","doi":"10.1016/j.physd.2024.134404","DOIUrl":"10.1016/j.physd.2024.134404","url":null,"abstract":"<div><div>A unified semi-analytical solution is presented for constructing the phase space near collinear libration points in the Circular Restricted Three-body Problem (CRTBP), encompassing Lissajous orbits, quasihalo orbits, Axial orbits, and their invariant manifolds, as well as transit and non-transit orbits. Based on classical in-plane and out-of-plane frequency resonance mechanisms, the Lindstedt–Poincaré method could only derive separate analytical solutions for the invariant manifolds of Lissajous orbits and halo orbits, falling short for the invariant manifolds of quasihalo orbits. In this paper, by introducing a coupling coefficient <em>η</em> and a bifurcation equation, a unified series solution for these orbits is systematically developed using a coupling-induced bifurcation mechanism and Lindstedt–Poincaré method. Analyzing the bifurcation equation obtained from different coupling forms reveals bifurcation conditions for all kinds of orbits near collinear libration points. When <em>η</em> = 0, the series solution describes non-bifurcated orbits, while when <em>η</em> ≠ 0, the solution describes bifurcated orbits, including quasihalo orbits, Axial orbits, and their invariant manifolds, as well as newly bifurcated transit and non-transit orbits. This unified semi-analytical framework provides a more comprehensive understanding of the complex phase space structures near collinear libration points in the CRTBP.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446039","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 : 2024-10-10DOI: 10.1016/j.physd.2024.134398
Yaru Xu , Xianguo Geng , Yunyun Zhai
The hierarchy of the semi-discrete Boussinesq equations associated with a discrete 4 × 4 matrix spectral problem has been derived by means of the zero-curvature and the Lenard recursion equations. The tetragonal curve is introduced by resorting to the characteristic polynomial of the Lax matrix for the semi-discrete Boussinesq hierarchy, upon which the Baker-Akhiezer functions, meromorphic functions, Abel differentials, and Riemann theta functions are constructed. Finally, we derive the Riemann theta function solutions to the semi-discrete Boussinesq hierarchy.
{"title":"Riemann theta function solutions to the semi-discrete Boussinesq equations","authors":"Yaru Xu , Xianguo Geng , Yunyun Zhai","doi":"10.1016/j.physd.2024.134398","DOIUrl":"10.1016/j.physd.2024.134398","url":null,"abstract":"<div><div>The hierarchy of the semi-discrete Boussinesq equations associated with a discrete 4 × 4 matrix spectral problem has been derived by means of the zero-curvature and the Lenard recursion equations. The tetragonal curve is introduced by resorting to the characteristic polynomial of the Lax matrix for the semi-discrete Boussinesq hierarchy, upon which the Baker-Akhiezer functions, meromorphic functions, Abel differentials, and Riemann theta functions are constructed. Finally, we derive the Riemann theta function solutions to the semi-discrete Boussinesq hierarchy.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446038","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 : 2024-10-10DOI: 10.1016/j.physd.2024.134402
Martin Donati , Ludovic Godard-Cadillac , Dragoş Iftimie
In this paper, we study the point-vortex dynamics with positive intensities. We show that in the half-plane and in a disk, collapses of point vortices with the boundary in finite time are impossible, hence the solution of the dynamics is global in time. We also give some necessary conditions for the existence of collapses with the boundary in general smooth bounded domains, in particular, that the trajectory of at least one point vortex has no limit. Some minor results are obtained with unsigned intensities.
{"title":"On the dynamics of point vortices with positive intensities collapsing with the boundary","authors":"Martin Donati , Ludovic Godard-Cadillac , Dragoş Iftimie","doi":"10.1016/j.physd.2024.134402","DOIUrl":"10.1016/j.physd.2024.134402","url":null,"abstract":"<div><div>In this paper, we study the point-vortex dynamics with positive intensities. We show that in the half-plane and in a disk, collapses of point vortices with the boundary in finite time are impossible, hence the solution of the dynamics is global in time. We also give some necessary conditions for the existence of collapses with the boundary in general smooth bounded domains, in particular, that the trajectory of at least one point vortex has no limit. Some minor results are obtained with unsigned intensities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529654","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 : 2024-10-10DOI: 10.1016/j.physd.2024.134400
Marc Jornet , Juan J. Nieto
We deal with a nonlinear stochastic fractional differential equation, in the Caputo and Itô senses, that generalizes important models of fluid dynamics, such as the Bagley–Torvik and the Basset equations. We investigate the integral formulation, existence, uniqueness, moment bounds, and continuity with respect to input data. Some conjectures are raised.
{"title":"On a nonlinear stochastic fractional differential equation of fluid dynamics","authors":"Marc Jornet , Juan J. Nieto","doi":"10.1016/j.physd.2024.134400","DOIUrl":"10.1016/j.physd.2024.134400","url":null,"abstract":"<div><div>We deal with a nonlinear stochastic fractional differential equation, in the Caputo and Itô senses, that generalizes important models of fluid dynamics, such as the Bagley–Torvik and the Basset equations. We investigate the integral formulation, existence, uniqueness, moment bounds, and continuity with respect to input data. Some conjectures are raised.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.physd.2024.134396
Zhicheng Zhang , Yan Zhang , Yingxue Du
Traditionally, stochastic disturbances arising in complex networks are often assumed to be drawn from a Wiener process, potentially limiting their applicability in real engineering scenarios. To address this limitation, we incorporate randomness to quantify the stochastic disturbances within a group of participating individuals, thereby establishing random nonlinear complex networks in a directed interacting setting. Subsequently, we demonstrate that the maximal existence interval of the unique solution to the underlying systems is determined by the properties of the associated noise and the specified Lipschitz constant. Building on this, we further show that, by making use of supermartingale and Lyapunov-based techniques, the almost sure synchronization condition of the investigated random complex system is determined by the communication topology, weight gain, and the number of participating agents. Additionally, we discuss synchronization problems within strongly connected and undirected graphs. Finally, we validate the proposed method using Chen systems.
{"title":"On synchronization of random nonlinear complex networks","authors":"Zhicheng Zhang , Yan Zhang , Yingxue Du","doi":"10.1016/j.physd.2024.134396","DOIUrl":"10.1016/j.physd.2024.134396","url":null,"abstract":"<div><div>Traditionally, stochastic disturbances arising in complex networks are often assumed to be drawn from a Wiener process, potentially limiting their applicability in real engineering scenarios. To address this limitation, we incorporate randomness to quantify the stochastic disturbances within a group of participating individuals, thereby establishing random nonlinear complex networks in a directed interacting setting. Subsequently, we demonstrate that the maximal existence interval of the unique solution to the underlying systems is determined by the properties of the associated noise and the specified Lipschitz constant. Building on this, we further show that, by making use of supermartingale and Lyapunov-based techniques, the almost sure synchronization condition of the investigated random complex system is determined by the communication topology, weight gain, and the number of participating agents. Additionally, we discuss synchronization problems within strongly connected and undirected graphs. Finally, we validate the proposed method using Chen systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529725","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 : 2024-10-09DOI: 10.1016/j.physd.2024.134399
Ziyang Zhang , Feifan Zhang , Weixi Gong , Tailai Chen , Luowei Tan , Heng Gui
Several classic reaction-diffusion models using partial differential equations (PDEs) have been established to elucidate the formation mechanism of vegetation patterns. However, predictive modeling of complex spatiotemporal dynamics using traditional numerical methods can be significantly challenging in many practical scenarios. Physics-Informed Neural Networks (PINNs) provide a new approach to predict the solution of PDEs. However, the generalization of PINNs is not satisfactory when pretrained PINNs is directly used in non-trained space (defined as explorations). This may be attributed to the lack of training in the time dimension. Therefore, a framework (LA-PINNs) is proposed to predict the evolutionary solution of the non-dimensional vegetation-sand model. The framework couples neural networks of Long-Short Terms Memory, Auto-Encoder and Physics-Informed Neural Networks. The predictions of LA-PINNs are much better than those of PINNs. Then we studied the effects of hyperparameters on the accuracy of predictions. Based on training in time dimension by LSTM module and pretraining for quick-training strategy, LA-PINNs can improve the accuracy of explorations.
{"title":"Prediction of spatiotemporal dynamics using deep learning: Coupled neural networks of long short-terms memory, auto-encoder and physics-informed neural networks","authors":"Ziyang Zhang , Feifan Zhang , Weixi Gong , Tailai Chen , Luowei Tan , Heng Gui","doi":"10.1016/j.physd.2024.134399","DOIUrl":"10.1016/j.physd.2024.134399","url":null,"abstract":"<div><div>Several classic reaction-diffusion models using partial differential equations (PDEs) have been established to elucidate the formation mechanism of vegetation patterns. However, predictive modeling of complex spatiotemporal dynamics using traditional numerical methods can be significantly challenging in many practical scenarios. Physics-Informed Neural Networks (PINNs) provide a new approach to predict the solution of PDEs. However, the generalization of PINNs is not satisfactory when pretrained PINNs is directly used in non-trained space (defined as explorations). This may be attributed to the lack of training in the time dimension. Therefore, a framework (LA-PINNs) is proposed to predict the evolutionary solution of the non-dimensional vegetation-sand model. The framework couples neural networks of Long-Short Terms Memory, Auto-Encoder and Physics-Informed Neural Networks. The predictions of LA-PINNs are much better than those of PINNs. Then we studied the effects of hyperparameters on the accuracy of predictions. Based on training in time dimension by LSTM module and pretraining for quick-training strategy, LA-PINNs can improve the accuracy of explorations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446040","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 : 2024-10-05DOI: 10.1016/j.physd.2024.134394
Yong Liu , Jun-Cheng Wei , Wen Yang
There are various different ways to obtain traveling waves of lump type(higher order lumps) for the KP-I equation. We propose a general and simple approach to derive them via a Bäcklund transformation. This enables us to establish an explicit connection between those lower energy solutions and higher energy ones. Based on this construction, spectral analysis of the degree 6 solutions is then carried out in details. The analysis of higher energy ones can be done in an inductive way.
{"title":"Lump type solutions: Bäcklund transformation and spectral properties","authors":"Yong Liu , Jun-Cheng Wei , Wen Yang","doi":"10.1016/j.physd.2024.134394","DOIUrl":"10.1016/j.physd.2024.134394","url":null,"abstract":"<div><div>There are various different ways to obtain traveling waves of lump type(higher order lumps) for the KP-I equation. We propose a general and simple approach to derive them via a Bäcklund transformation. This enables us to establish an explicit connection between those lower energy solutions and higher energy ones. Based on this construction, spectral analysis of the degree 6 solutions is then carried out in details. The analysis of higher energy ones can be done in an inductive way.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433542","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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