Coherent structures of some \((1+1)\)-dimensional nonlinear systems

DOI10.1016/j.physleta.2005.03.015zbMath1137.35305OpenAlexW2169272067MaRDI QIDQ2478880

Zuliang Pan, Jun Zhang, Shou-feng Shen

Publication date: 25 March 2008

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2005.03.015

zbMATH Keywords

nonlinear systemcoherent structureBäcklund transformationvariable separation

Mathematics Subject Classification ID

Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

Novel variable separation solutions and exotic localized excitations via the ETM in nonlinear soliton systems ⋮ New exact solutions with an arbitrary function of two \((1+1)\)-dimensional nonlinear evolution equations ⋮ Lie symmetry analysis and Painlevé analysis of the new \((2+1)\)-dimensional KdV equation ⋮ Exotic localized structures based on variable separation solution of \((2+1)\)-dimensional KdV equation via the extended tanh-function method ⋮ Nonlinear evolution equations admitting multilinear variable separable solutions ⋮ Bäcklund transformations and solutions of some generalized nonlinear evolution equations ⋮ New \((2 + 1)\)-dimensional sine-Gordon equation with self-consistent sources derived by the nonlinear variable separation method ⋮ The Davey-Stewartson equation with sources derived from nonlinear variable separation method ⋮ Nonlinear variable separation solutions of some mKdV-type equations and the unified construction method ⋮ A method for constructing nontraveling wave solutions for (1+1)-dimensional evolution equations ⋮ NEW TYPES OF INTERACTIONS BASED ON VARIABLE SEPARATION SOLUTIONS VIA THE GENERAL PROJECTIVE RICCATI EQUATION METHOD

Cites Work

• On the coherent structures of the Nizhnik-Novikov-Veselov equation
• On two-dimensional packets of capillary-gravity waves
• Variable separation approach for a differential-difference system: special Toda equation
• A Generalization of Coupled Integrable, Dispersionless System
• Lagrangian, Hamiltonian and Conserved Quantities for Coupled Integrable, Dispersionless Equations
• Resonant two-wave interaction in the Davydov model
• Extended multilinear variable separation approach and multivalued localized excitations for some (2+1)-dimensional integrable systems
• High-dimensional Virasoro integrable models and exact solutions