The approximate solution for Benjamin-Bona-Mahony equation under slowly varying medium

Wenxia Chen; Ping Yang; Weiwei Gao; Lixin Tian

doi:10.3934/cpaa.2018042

Article Contents

2018, Volume 17, Issue 3: 823-848. Doi: 10.3934/cpaa.2018042

This issue Previous Article Symmetry and non-existence of solutions to an integral system Next Article Existence results for the fractional Q-curvature problem on three dimensional CR sphere

The approximate solution for Benjamin-Bona-Mahony equation under slowly varying medium

1.
Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
2.
School of Mathematical Science, Nanjing Normal University, Nanjing, Jiangsu, 210023, China

* Corresponding author: Wenxia Chen
* Corresponding author: Wenxia Chen

Received: May 31, 2017

Revised: September 30, 2017

Published: May 2018

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Abstract

In this paper, we investigate the soliton dynamics under slowly varying medium for the BBM equation, that is how the solution of this equation evolve when the time goes. We construct the approximate solution of this equation and prove that the error term due to the approximate solution can be controlled. By using the method of Lyapunov and Weinstein functions, we prove that the approximate solution is stable.

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Mathematics Subject Classification: Primary: 35Q53, 35B40.

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References

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