Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions-Reference-Cited by-同舟云学术

Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions

Published:2022 Issue:7 Volume:42 Page:3355
ISSN:1078-0947
Container-title:Discrete and Continuous Dynamical Systems
language:
Short-container-title:DCDS

Author:

Gong Ruizhi¹²,Shi Yuren³,Wang Deng-Shan¹

Affiliation:

1. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

2. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

3. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

Abstract

<p style='text-indent:20px;'>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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference36 articles.

1. M. J. Ablowitz, P. A. Clarkson., Solitons, Nonlinear Evolution Equations and Inverse Scattering, ${ref.volume} (1991).

2. R. Balakrishnan, I. I. Satija.Solitons in Bose-Einstein condensates, Pramana J. Phys., 77 (2011), 929-947.

3. C. Charlier and J. Lenells, The "good" Boussinesq equation: A Riemann-Hilbert approach, Indiana Univ. Math. J., to appear 2021, arXiv: 2003.02777, 48 pp.

4. C. Charlier, J. Lenells and D. S. Wang, The "good" Boussinesq equation: Long-time asymptotics, Analysis & PDE, to appear 2021, arXiv: 2003.04789, 34 pp.

5. T. Congy, S. K. Ivanov, A. M. Kamchatnov and N. Pavloff, Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion, Chaos, 27 (2017), Paper No. 083107, 12 pp.

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