Reduction to modified KdV and its KP-like generalization via phase modulation
Reduction to modified KdV and its KP-like generalization via phase modulation
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DOI：
10.1088/1361-6544/aabfab
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发表时间：
2018-07
期刊：
影响因子：
1.7
通讯作者：
D. Ratliff;T. Bridges
中科院分区：
文献类型：
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作者：
D. Ratliff;T. Bridges
本文的主要观察是，修改后的Korteweg-de弗里斯方程有其自然的起源在相位调制的基本状态，如周期性行波，或更一般地说，家庭的相对平衡。扩展到2 + 1表明，一个修改的Kadomtsev-Petviashvili（或Konopelchenko-Dubrovsky）方程应该出现，但我们的结果表明，有一个额外的条款，这是迄今为止没有注意到。因此，通过相位调制的新应用，一个新的方程出现作为2 + 1扩展到以前已知的。为了证明该理论，它被应用到五阶非线性薛定谔（CQNLS）方程，表明有相关的参数值，修改后的KP方程从2 + 1 CQNLS方程的周期行波解分叉。
The main observation of this paper is that the modified Korteweg–de Vries equation has its natural origin in phase modulation of a basic state such as a periodic travelling wave, or more generally, a family of relative equilibria. Extension to 2 + 1 suggests that a modified Kadomtsev–Petviashvili (or a Konopelchenko–Dubrovsky) equation should emerge, but our result shows that there is an additional term which has gone heretofore unnoticed. Thus, through the novel application of phase modulation a new equation appears as the 2 + 1 extension to a previously known one. To demonstrate the theory it is applied to the cubic-quintic nonlinear Schrödinger (CQNLS) equation, showing that there are relevant parameter values where a modified KP equation bifurcates from periodic travelling wave solutions of the 2 + 1 CQNLS equation.