EXISTENCE OF SOLITARY WAVES AND PERIODIC WAVES TO A PERTURBED GENERALIZED KDV EQUATION

DOI10.3846/13926292.2014.960016zbMath1488.34329OpenAlexW1996316724MaRDI QIDQ5011198

Yong Liang, Weifang Yan, Zheng-Rong Liu

Publication date: 27 August 2021

Published in: Mathematical Modelling and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3846/13926292.2014.960016

zbMATH Keywords

traveling wavesgeometric singular perturbation theoryregular perturbation analysis for a Hamiltonian systemperturbed generalized KdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Singular perturbations for ordinary differential equations (34E15) Traveling wave solutions (35C07) Bifurcation of solutions to ordinary differential equations involving randomness (34F10)

Related Items (21)

Existence of kink waves and periodic waves for a perturbed defocusing mKdV equation ⋮ The solitary wave, kink and anti-kink solutions coexist at the same speed in a perturbed nonlinear Schrödinger equation ⋮ A hybridized discontinuous Galerkin method for the nonlinear Korteweg-de Vries equation ⋮ Existence of solitary waves and periodic waves for a perturbed generalized BBM equation ⋮ Existence of periodic waves for a perturbed quintic BBM equation ⋮ Persistence of kink and periodic waves to singularly perturbed two-component Drinfel'd-Sokolov-Wilson system ⋮ Existence of periodic wave of a BBM equation with delayed convection and weak diffusion ⋮ Solitary waves of singularly perturbed generalized KdV equation with high order nonlinearity ⋮ Traveling waves in a quintic BBM equation under both distributed delay and weak backward diffusion ⋮ Existence of traveling wave solutions for a generalized Burgers-Fisher equation with weak convection ⋮ On the monotonicity of limit wave speed of the pgKdV equation with nonlinear terms of arbitrary higher degree ⋮ Existence of single-peak solitary waves and double-peaks solitary wave of Gardner equation with Kuramoto-Sivashinsky perturbation ⋮ Limit speed of traveling wave solutions for the perturbed generalized KdV equation ⋮ Existence of traveling waves in a delayed convecting shallow water fluid model ⋮ Monotonicity of limit wave speed of traveling wave solutions for a perturbed generalized KdV equation ⋮ Some smooth and nonsmooth traveling wave solutions for KP-\(\mathrm{MEW}(2, 2)\) equation ⋮ Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms ⋮ An unconditionally stable space-time FE method for the Korteweg-de Vries equation ⋮ Existence of solitary waves in a perturbed KdV-mKdV equation ⋮ A New Type of Solitary Wave Solution of the mKdV Equation Under Singular Perturbations ⋮ Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation

Cites Work

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