Qualitative analysis to traveling wave solutions of Zakharov–Kuznetsov–Burgers equation and its damped oscillatory solutions

作者：

Highlights：

• The uniqueness of the bounded traveling wave solution is proved for ZKB equation.

• We give a critical value d0 characterizing the scale of dissipation effect.

• We obtain the approximate damped oscillatory solution.

• We present the error estimate between approximate solution and its exact solution.

• The method in this paper can also be applied to KdV–Burgers equation.

摘要

•The uniqueness of the bounded traveling wave solution is proved for ZKB equation.•We give a critical value d0 characterizing the scale of dissipation effect.•We obtain the approximate damped oscillatory solution.•We present the error estimate between approximate solution and its exact solution.•The method in this paper can also be applied to KdV–Burgers equation.

论文关键词：Zakharov–Kuznetsov–Burgers equation,Planar dynamical system,Damped oscillatory solution,Error estimate

论文评审过程：Available online 4 April 2014.

论文官网地址：https://doi.org/10.1016/j.amc.2014.02.082