Open AccessLinear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions
Author(s) -
Ruizhi Gong,
Yu-Ren Shi,
DengShan Wang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2022018
Subject(s) - integrable system , stability (learning theory) , traveling wave , linear stability , mathematics , exact solutions in general relativity , mathematical analysis , physics , nonlinear system , quantum mechanics , computer science , machine learning
The integrability, classification of traveling wave solutions and stability of exact solutions for the generalized Kaup-Boussinesq equation are studied by prolongation structure technique and linear stability analysis. Firstly, it is proved that the generalized Kaup-Boussinesq equation is completely integrable in sense of having Lax pair. Secondly, the complete classification of exact traveling wave solutions of the generalized Kaup-Boussinesq equation are given and a family of exact solutions are proposed. Finally, the stability of these exact solutions are investigated by linear stability analysis and dynamical evolutions, and some stable traveling wave solutions are found. It is shown that the results of linear stability analysis are in excellent agreement with the results from dynamical evolutions.