Continuation methods for time-periodic travelling-wave solutions to evolution equations
Continuation methods for time-periodic travelling-wave solutions to evolution equations
复制标题
DOI：
10.1016/j.aml.2018.06.034
复制
发表时间：
2018-12
期刊：
影响因子：
--
通讯作者：
Te-Sheng Lin;D. Tseluiko;M. Blyth;S. Kalliadasis
中科院分区：
文献类型：
--
作者：
Te-Sheng Lin;D. Tseluiko;M. Blyth;S. Kalliadasis
发展了一种数值延拓方法来跟踪局部和非局部发展偏微分方程的时间周期行波解。它被发现，运动坐标的速度方程可以自然地从控制方程连同打破平移对称性的条件。导出的方程组允许人们遵循行波解的分支以及在以恒定速度行进的参考系中具有时间周期性的解。最后，以带电降膜长波模型为例，给出了单脉冲波和双脉冲波的分岔和稳定性分析。
A numerical continuation method is developed to follow time-periodic travelling-wave solutions of both local and non-local evolution partial differential equations (PDEs). It is found that the equation for the speed of the moving coordinate can be derived naturally from the governing equations together with a condition that breaks the translational symmetry. The derived system of equations allows one to follow the branch of travelling-wave solutions as well as solutions that are time-periodic in a frame of reference travelling at a constant speed. Finally, we show as an example the bifurcation and stability analysis of single and double-pulse waves in long-wave models of electrified falling films.