New traveling wave solutions and interesting bifurcation phenomena of generalized KdV-mKdV-like equation
type: Item
instance of: scholarly article
title: New traveling wave solutions and interesting bifurcation phenomena of generalized KdV-mKdV-like equation
zbMATH Open document ID: 1483.35184
DOI: 10.1155/2021/4213939
author: Shaoyong Li
author: Yi-ren Chen
published in: Advances in Mathematical Physics
publication date: 2022-01-06T00:00:00Z
review text: Summary: Using the bifurcation method of dynamical systems, we investigate the nonlinear waves and their limit properties for the generalized KdV-mKdV-like equation. We obtain the following results: (i) three types of new explicit expressions of nonlinear waves are obtained. (ii) Under different parameter conditions, we point out these expressions represent different waves, such as the solitary waves, the 1-blow-up waves, and the 2-blow-up waves. (iii) We revealed a kind of new interesting bifurcation phenomenon. The phenomenon is that the 1-blow-up waves can be bifurcated from 2-blow-up waves. Also, we gain other interesting bifurcation phenomena. We also show that our expressions include existing results.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 7452836
zbMATH Keywords: generalized KdV-mKdV-like equation
zbMATH Keywords: traveling wave
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/4213939
OpenAlex ID: W3215016113
cites work: Global solutions and large time behavior for the chemotaxis-shallow water system
cites work: The robust inverse scattering method for focusing Ablowitz-Ladik equation on the non-vanishing background
cites work: Computing solitary wave solutions of coupled nonlinear Hirota and Helmholtz equations
cites work: A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms
cites work: Constructing of new exact solutions to the GKdV-mKdV equation with any-order nonlinear terms by \((\frac{G'}{G})\)-expansion method
cites work: Solitary wave solutions and kink wave solutions for a generalized KdV-mKdV equation
cites work: The Korteweg–deVries Equation: A Survey of Results
cites work: Two new classes of exact solutions for the KdV equation via Bäcklund transformations
cites work: An explicit formula for a class of solutions of the KdV equation
cites work: Lie–Bäcklund symmetries of certain nonlinear evolution equations under perturbation around their solutions
cites work: Solitary wave solutions of the MKdV\(^-\) equation
cites work: Explicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order.
cites work: Construction of non-analytic solutions for the generalized KdV equation
cites work: A note on the Lie symmetry analysis and exact solutions for the extended mKdV equation
cites work: Singular solution in a damped double sinh-Gordon system
cites work: Q3469607
cites work: Generation of large-amplitude solitons in the extended Korteweg–de Vries equation
cites work: Trigonometric function periodic wave solutions and their limit forms for the KdV-like and the PC-like equations
cites work: BIFURCATIONS OF SOLITARY WAVES AND DOMAIN WALL WAVES FOR KdV-LIKE EQUATION WITH HIGHER ORDER NONLINEARITY
cites work: Traveling wave solutions of space-time fractional generalized fifth-order KdV equation
cites work: Bifurcations and Exact Traveling Wave Solutions of the Celebrated Green–Naghdi Equations
cites work: Bifurcation analysis for ion acoustic waves in a strongly coupled plasma including trapped electrons
cites work: Bifurcations of Solitary Waves of a Simple Equation
description: scientific article; zbMATH DE number 7452836