Spectral stability theory of heteroclinic solutions to the Korteweg-de Vries-Burgers equation with an arbitrary potential
type: Item
instance of: scholarly article
title: Spectral stability theory of heteroclinic solutions to the Korteweg-de Vries-Burgers equation with an arbitrary potential
zbMATH Open document ID: 1368.35235
DOI: 10.1134/S0081543816080083
author: A. P. Chugaĭnova
author: A. T. Il'ichev
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2017-04-11T00:00:00Z
review text: The authors study the linear stability of travelling waves of the generalized Korteweg-de Vries-Burgers equation \(v_t+\varphi(v)_x=\mu v_{xx}-mv_{xxx}\) with a general function \(\varphi\). An example of a nonconvex potential \(\varphi\) is given with many heteroclinic solutions of different types.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 6704064
zbMATH Keywords: generalized Korteweg-de Vries-Burgers equation
zbMATH Keywords: travelling waves
zbMATH Keywords: heteroclinic solution
zbMATH Keywords: linear stability
MaRDI profile type: Publication
cites work: Q4850474
cites work: Nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation
cites work: Q4557258
cites work: Stability of nonstationary solutions of the generalized KdV-Burgers equation
cites work: Stability of discontinuity structures described by a generalized KdV-Burgers equation
cites work: Q3274320
cites work: Q5726858
cites work: Q4425058
cites work: Envelope solitary waves and dark solitons at a water-ice interface
cites work: Soliton-like structures on a water-ice interface
cites work: Solitary wave packets beneath a compressed ice cover
cites work: Spectral stability of special discontinuities
cites work: Stability of an inflated hyperelastic membrane tube with localized wall thinning
cites work: Q5691916
cites work: Classical and non-classical discontinuities in solutions of equations of non-linear elasticity theory
cites work: Q4527762
cites work: Oscillatory instability of traveling waves for a KdV-Burgers equation
cites work: Eigenvalues, and instabilities of solitary waves
full work available at URL: s0081543816080083
OpenAlex ID: W2581957080
description: scientific article; zbMATH DE number 6704064