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September/October 2011 Existence of traveling-wave solutions to Boussinesq systems
Min Chen, Nghiem V. Nguyen, Shu-Ming Sun
Differential Integral Equations 24(9/10): 895-908 (September/October 2011).

Abstract

In this manuscript, the existence of traveling-wave solutions to Boussinesq systems \begin{equation*} \left\{ \begin{matrix} \eta_t +u_x+(\eta u)_x +au_{xxx}-b \eta_{xxt}=0, &\\ u_t + \eta_x +uu_x +c\eta_{xxx} - d u_{xxt}=0,&\\ \end{matrix} \right. \end{equation*} is established. We prove that all the systems with $ a<0,$ $ c<0$ and $ b=d$ exhibit traveling-wave solutions with small propagation speeds. The result complements our earlier work [6] on a restricted family of the systems where both existence and stability of traveling-wave solutions were established in the presence of large surface tension, namely when $a+b+c+d<0$.

Citation

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Min Chen. Nghiem V. Nguyen. Shu-Ming Sun. "Existence of traveling-wave solutions to Boussinesq systems." Differential Integral Equations 24 (9/10) 895 - 908, September/October 2011.

Information

Published: September/October 2011
First available in Project Euclid: 20 December 2012

zbMATH: 1249.35286
MathSciNet: MR2850344

Subjects:
Primary: 35A15, 35B35, 35Q35

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.24 • No. 9/10 • September/October 2011
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