Solitary wave solutions of the high-order KdV models for bi-directional water waves

DOI10.1016/j.cnsns.2010.06.032zbMath1221.35327OpenAlexW2068885963MaRDI QIDQ718441

Georgy I. Burde

Publication date: 23 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2010.06.032

zbMATH Keywords

solitary wave solutionswater wave modelshigh-order KdV equationsLie-Bäcklund groups

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Soliton solutions (35C08)

Related Items (6)

One- and two-soliton solutions to a new KdV evolution equation with nonlinear and nonlocal terms for the water wave problem ⋮ Two structure-preserving schemes with fourth-order accuracy for the modified Kawahara equation ⋮ A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau-Kawahara-RLW equation ⋮ Orbital stability and dynamical behaviors of solitary waves for the Camassa-Holm equation with quartic nonlinearity ⋮ Effects of viscosity and surface tension on soliton dynamics in the generalized KdV equation for shallow water waves ⋮ Solitary wave solution and a linear mass-conservative difference scheme for the generalized Korteweg-de Vries-Kawahara equation

Cites Work

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• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• On the asymptotic solutions of the KdV equation with higher-order corrections
• Model equations for long waves in nonlinear dispersive systems
• Symmetries and differential equations

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