Integrable nonlocal asymptotic reductions of physically significant nonlinear equations
Integrable nonlocal asymptotic reductions of physically significant nonlinear equations
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DOI：
10.1088/1751-8121/ab0e95
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发表时间：
2019-03
期刊：
影响因子：
--
通讯作者：
M. Ablowitz;Z. Musslimani
中科院分区：
文献类型：
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作者：
M. Ablowitz;Z. Musslimani
得到了一些物理上重要的方程的拟单色复约化。从三次非线性Klein-Gordon(NLKG)方程、Korteweg-de Vries(KdV)方程和水波方程出发，证明了导数阶渐近近似可以转化为著名的可积AKNS系统(Ablwitz等，1974，Stud)。APPL数学课。53 249)与二阶(空间)非线性波动方程有关。这反过来又第一次在最近发现的AKNS系统的非局部可积约化和物理上有趣的方程之间建立了重要的物理联系。约化包括宇称时间方程、逆时空方程和逆时非局域非线性薛定谔方程。
Quasi-monochromatic complex reductions of a number of physically important equations are obtained. Starting from the cubic nonlinear Klein–Gordon (NLKG), the Korteweg–de Vries (KdV) and water wave equations, it is shown that the leading order asymptotic approximation can be transformed to the well-known integrable AKNS system (Ablowitz et al 1974 Stud. Appl. Math. 53 249) associated with second order (in space) nonlinear wave equations. This in turn establishes, for the first time, an important physical connection between the recently discovered nonlocal integrable reductions of the AKNS system and physically interesting equations. Reductions include the parity-time, reverse space-time and reverse time nonlocal nonlinear Schrödinger equations.