Multi-lump formations from lump chains and plane solitons in the KP1 equation

[1]  Junchao Chen,et al.  Peculiarities of resonant interactions of lump chains within the KP1 equation , 2022, Physica Scripta.

[2]  Junchao Chen,et al.  The nonlinear superposition between anomalous scattering of lumps and other waves for KPI equation , 2022, Nonlinear Dynamics.

[3]  Junchao Chen,et al.  Degenerate lump interactions within the Kadomtsev-Petviashvili equation , 2022, Commun. Nonlinear Sci. Numer. Simul..

[4]  S. Chakravarty,et al.  Classification of KPI lumps , 2022, Journal of Physics A: Mathematical and Theoretical.

[5]  Junchao Chen,et al.  Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation , 2022, Communications in Theoretical Physics.

[6]  J. Rao,et al.  Resonant collisions between lumps and periodic solitons in the Kadomtsev–Petviashvili I equation , 2022, Journal of Mathematical Physics.

[7]  Jianke Yang,et al.  Rogue waves in (2+1)-dimensional three-wave resonant interactions , 2021, Physica D: Nonlinear Phenomena.

[8]  Jianke Yang,et al.  Pattern Transformation in Higher-Order Lumps of the Kadomtsev–Petviashvili I Equation , 2021, Journal of Nonlinear Science.

[9]  Liming Ling,et al.  Kadomtsev–Petviashvili equation: One-constraint method and lump pattern , 2021, Physica D: Nonlinear Phenomena.

[10]  Y. Stepanyants,et al.  Lump Interactions with Plane Solitons , 2021, Radiophysics and Quantum Electronics.

[11]  S. Chakravarty,et al.  Dynamics of KPI lumps , 2021, Journal of Physics A: Mathematical and Theoretical.

[12]  K. Chow,et al.  Completely resonant collision of lumps and line solitons in the Kadomtsev–Petviashvili I equation , 2021, Studies in Applied Mathematics.

[13]  Junchao Chen,et al.  Construction of higher-order smooth positons and breather positons via Hirota’s bilinear method , 2021, Nonlinear Dynamics.

[14]  Jianke Yang,et al.  Universal rogue wave patterns associated with the Yablonskii–Vorob’ev polynomial hierarchy , 2021, 2103.11223.

[15]  V. Zakharov,et al.  Lump chains in the KP‐I equation , 2021, Studies in Applied Mathematics.

[16]  Jianke Yang,et al.  Rogue wave patterns in the nonlinear Schrödinger equation , 2021, Physica D: Nonlinear Phenomena.

[17]  Jingsong He,et al.  Degeneration of breathers in the Kadomttsev-Petviashvili I equation , 2020, Commun. Nonlinear Sci. Numer. Simul..

[18]  Zhiming Lu,et al.  Interaction of multi-lumps within the Kadomtsev–Petviashvili equation , 2018 .

[19]  Jingsong He,et al.  Generation of higher-order rogue waves from multibreathers by double degeneracy in an optical fiber. , 2017, Physical review. E.

[20]  Jingsong He,et al.  Rogue Waves and Hybrid Solutions of the Boussinesq Equation , 2017 .

[21]  Zhenya Yan,et al.  Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations , 2016, Commun. Nonlinear Sci. Numer. Simul..

[22]  Y. Kodama KP Solitons and the Grassmannians , 2017 .

[23]  P. Clarkson,et al.  Rational solutions of the Boussinesq equation and applications to rogue waves , 2016, 1609.00503.

[24]  A. Fokas,et al.  Generating mechanism for higher-order rogue waves. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Q. P. Liu,et al.  Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  L. Debnath Solitons and the Inverse Scattering Transform , 2012 .

[27]  Vladimir E. Zakharov,et al.  Turbulence in Integrable Systems , 2009 .

[28]  R. Grimshaw,et al.  Interaction of two lump solitons described by the Kadomtsev–Petviashvili I equation , 2004 .

[29]  Dmitry Pelinovsky,et al.  Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations , 2004, SIAM J. Numer. Anal..

[30]  Vladimir E. Zakharov,et al.  The Boussinesq equation revisited , 2002 .

[31]  Y. Ohta,et al.  Determinant structure of the rational solutions for the Painlevé II equation , 1996, solv-int/9709011.

[32]  Y. Stepanyants,et al.  The structure of the rational solutions to the Boussinesq equation , 1995 .

[33]  Y. Stepanyants,et al.  Normal and anomalous scattering, formation and decay of bound states of two-dimensional solitons described by the Kadomtsev-Petviashvili equation , 1993 .

[34]  Y. Murakami,et al.  Rational growing mode : exact solutions to the Boussinesq equation , 1991 .

[35]  Y. Stepanyants,et al.  Two-dimensional multisolitons: Stationary solutions of Kadomtsev - Petviashvili equation , 1985 .

[36]  S. Zhdanov,et al.  Soliton chains in a plasma with magnetic viscosity , 1984 .

[37]  A. Zaitsev Formation of stationary nonlinear waves by superposition of solitons , 1984 .

[38]  J. Satsuma,et al.  Two‐dimensional lumps in nonlinear dispersive systems , 1979 .

[39]  J. Satsuma Solitons and Rational Solutions of Nonlinear Evolution Equations (Theory of Nonlinear Waves) , 1978 .

[40]  Igor Krichever,et al.  Rational solutions of the Kadomtsev — Petviashvili equation and integrable systems of N particles on a line , 1978 .

[41]  Ljudmila A. Bordag,et al.  Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction , 1977 .

[42]  V. Petviashvili Equation of an extraordinary soliton , 1976 .

[43]  Vladimir E. Zakharov,et al.  A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I , 1974 .

[44]  B. Kadomtsev,et al.  On the Stability of Solitary Waves in Weakly Dispersing Media , 1970 .