Darboux transformation and nonautonomous solitons for a modified Kadomtsev-Petviashvili equation with variable coefficients

DOI10.1016/j.camwa.2018.03.022zbMath1420.35330OpenAlexW2794599507MaRDI QIDQ2001328

Lei Wang, Xin Wang

Publication date: 3 July 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.03.022

zbMATH Keywords

asymptotic analysisDarboux transformationMKP equation with variable coefficientsnonautonomous solitons

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Geometric theory, characteristics, transformations in context of PDEs (35A30) Soliton solutions (35C08)

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Cites Work

• Unnamed Item
• Quasi-periodic solutions to the hierarchy of four-component Toda lattices
• Breather interactions and higher-order nonautonomous rogue waves for the inhomogeneous nonlinear Schrödinger Maxwell-Bloch equations
• Binary Darboux transformation for a variable-coefficient nonisospectral modified Kadomtsev-Petviashvili equation with symbolic computation
• Multi-front waves for extended form of modified Kadomtsev-Petviashvili equation
• Generalized (2 + 1)-dimensional Gardner model: bilinear equations, Bäcklund transformation, Lax representation and interaction mechanisms
• Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations
• Linear superposition principle applying to Hirota bilinear equations
• Symbolic computation on cylindrical-modified dust-ion-acoustic nebulons in dusty plasmas
• Inelastic interactions of the multiple-front waves for the modified Kadomtsev-Petviashvili equation in fluid dynamics, plasma physics and electrodynamics
• A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures
• Parabola solitons for the nonautonomous KP equation in fluids and plasmas
• Determinant representation of Darboux transformation for the AKNS system
• Evolution of solitary waves in multicomponent plasmas
• Modified Kadomtsev-Petviashvili (MKP) equation and electromagnetic soliton
• Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation
• Abundant lump-type solutions of the Jimbo-Miwa equation in \((3+1)\)-dimensions
• Darboux transformation of the coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization
• Periodic and rational solutions of the reduced Maxwell-Bloch equations
• A vector generalization of Volterra type differential-difference equations
• Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation
• SOLITON RESONANCES FOR THE MODIFIED KADOMTSEV–PETVIASHVILI EQUATIONS IN UNIFORM AND NON-UNIFORM MEDIA
• Inverse Spectral Transform for the Modified Kadomtsev-Petviashvili Equation
• Darboux transformations via Painlevé analysis
• Rogue waves and W-shaped solitons in the multiple self-induced transparency system
• Two-dimensional Interaction of Solitary Waves in a Modified Kadomtsev–Petviashvili Equation
• Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation
• Integrability study on a generalized (2+1)-dimensional variable-coefficient Gardner model with symbolic computation

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