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

Wenxia Chen, Ping Yang, Weiwei Gao, Lixin Tian
2018 Communications on Pure and Applied Analysis  
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. 2000 Mathematics Subject Classification. Primary: 35Q53, 35B40.
doi:10.3934/cpaa.2018042 fatcat:yyawr6y2lbeyplov76mbynxhkq