Category of nonlinear evolution equations, algebraic structure, and r-matrix

DOI10.1063/1.1532769zbMath1061.37050arXivnlin/0201066OpenAlexW2094563325MaRDI QIDQ4832908

Zhijun Qiao, Ce Wen Cao, Walter Strampp

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0201066

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (17)

Two kinds of new integrable couplings of the negative-order Korteweg-de Vries equation ⋮ The Cauchy problem for a generalized two-component short pulse system with high-order nonlinearities ⋮ Soliton resolution for the Wadati-Konno-Ichikawa equation with weighted Sobolev initial data ⋮ Darboux transformation and solitonic solution to the coupled complex short pulse equation ⋮ Multi-soliton solutions and the Cauchy problem for a two-component short pulse system ⋮ Wadati-Konno-Ichikawa-type integrable systems and their constructions ⋮ Soliton interactions and Yang–Baxter maps for the complex coupled short‐pulse equation ⋮ Wave solutions to an integrable negative order KdV equation ⋮ Rogue periodic waves of the short pulse equation and the coupled integrable dispersionless equation ⋮ New interaction solutions and nonlocal symmetry of an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form ⋮ A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions ⋮ L-A-B representation for nonlinear evolution equations and its applications ⋮ Negative order MKdV hierarchy and a new integrable Neumann-like system ⋮ Nonlocal symmetry and Bäcklund transformation of a negative-order Korteweg-de Vries equation ⋮ New Bäcklund transformations of the \((2+1)\)-dimensional Bogoyavlenskii equation via localization of residual symmetries ⋮ Generalized negative flows in hierarchies of integrable evolution equations ⋮ On the soliton resolution and the asymptotic stability of \(N\)-soliton solution for the Wadati-Konno-Ichikawa equation with finite density initial data in space-time solitonic regions

Cites Work

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
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