Interactions among different types of nonlinear waves described by the Kadomtsev-Petviashvili equation

DOI10.1016/j.wavemoti.2014.07.012zbMath1456.35177arXiv1208.3259OpenAlexW2963273170MaRDI QIDQ1727662

Xue-Ping Cheng, Chun-Li Chen, Sen-yue Lou

Publication date: 20 February 2019

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3259

zbMATH Keywords

KP equationsymmetry reductionsnonlocal symmetriessoliton-Boussinesq wavesoliton-KdV wavesoliton-periodic wave

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Soliton solutions (35C08)

Related Items (14)

Bosonization, singularity analysis, nonlocal symmetry reductions and exact solutions of supersymmetric KdV equation ⋮ Bäcklund transformation and soliton-cnoidal wave interaction solution for the coupled Klein-Gordon equations ⋮ Consistent Riccati expansion solvability and soliton-cnoidal wave interaction solution of a \((2 + 1)\)-dimensional Korteweg-de Vries equation ⋮ New interaction solutions of \((3+1)\)-dimensional KP and \((2+1)\)-dimensional Boussinesq equations ⋮ Residual symmetries and interaction solutions for the Whitham-Broer-Kaup equation ⋮ Nonlocal symmetries and interaction solutions of the Benjamin-Ono equation ⋮ Interaction behavior between solitons and (\(2+1)\)-dimensional CDGKS waves ⋮ Generalized Darboux transformation for the discrete Kadomtsev-Petviashvili equation with self-consistent sources ⋮ Duality of positive and negative integrable hierarchies via relativistically invariant fields ⋮ Nonlocal symmetry, Darboux transformation and soliton-cnoidal wave interaction solution for the shallow water wave equation ⋮ Interaction solutions of a \((2+1)\)-dimensional dispersive long wave system ⋮ Residual symmetry reduction and consistent Riccati expansion to a nonlinear evolution equation ⋮ Interaction solutions for a dimensionally reduced Hirota bilinear equation ⋮ Characteristics of Rogue Waves on a Soliton Background in the General Coupled Nonlinear Schrödinger Equation

Cites Work

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• Applications of KdV
• Integration of the soliton hierarchy with self-consistent sources
• On the evolution of packets of water waves
• Nonlocal Symmetries for Bilinear Equations and Their Applications
• Construction of dKP and BKP equations with self-consistent sources
• Infinitely many Lax pairs and symmetry constraints of the KP equation
• Negative Kadomtsev–Petviashvili Hierarchy
• Non-local symmetries via Darboux transformations
• Virasoro structure and localized excitations of the LKR system
• Symmetries and differential equations

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