Modified Kortweg–de Vries hierarchies in multiple–time variables and the solutions of modified Boussinesq equations
Modified Kortweg–de Vries hierarchies in multiple–time variables and the solutions of modified Boussinesq equations
复制标题
多时间变量中修正的Kortweg-de Vries层次结构和修正的Boussinesq方程的解
DOI：
10.1098/rspa.1998.0215
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
V. Merle
中科院分区：
文献类型：
--
作者：
M. Manna;V. Merle
利用多重约化摄动方法研究了一类修正的Boussinesq方程的孤立波解和扭结波解。我们使用适当的修正的Korteweg-de Vries方程来消除微扰格式每一阶中的长期产生项。我们证明，在孤立波解的情况下，获得正则扰动级数所需的多重时间变量完全由相关的线性理论决定，但在扭结波解的情况下，需要知道扰动级数的每一阶。这些适当的多重时间变量使我们能够证明，修正的Boussinesq方程的孤立波解和扭结波解实际上分别是满足适当修正的Korteweg-de Vries族的所有方程的孤立波和扭结波。
We study solitary–wave and kink–wave solutions of a modified Boussinesq equation through a multiple–time reductive perturbation method. We use appropriated modified Korteweg–de Vries hierarchies to eliminate secular–producing terms in each order of the perturbative scheme. We show that the multiple–time variables needed to obtain a regular perturbative series are completely determined by the associated linear theory in the case of a solitary–wave solution, but require the knowledge of each order of the perturbative series in the case of a kink–wave solution. These appropriate multiple–time variables allow us to show that the solitary–wave as well as the kink–wave solutions of the modified Boussinesq equation are actually, respectively, a solitary–wave and a kink–wave satisfying all the equations of suitable modified Korteweg–de Vries hierarchies.