Dissipative Nonlinear Schrodinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution
Dissipative Nonlinear Schrodinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution
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分层流体中具有耗散效应的包络孤立罗斯贝波耗散非线性薛定谔方程及其解
DOI：
10.1155/2014/643652
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发表时间：
2014
影响因子：
--
通讯作者：
Xu Zhenhua
中科院分区：
文献类型：
--
作者：
Shi Yunlong;Yin Baoshu;Yang Hongwei;Yang Dezhou;Xu Zhenhua
利用多尺度分析和微扰方法求解了耗散非线性薛定谔方程，描述了分层流体中具有耗散效应的包络Rossby孤立波.通过分析包络Rossby孤立波振幅的演化，发现基流切变、Brunt-Vaisala频率和β效应是形成包络Rossby孤立波的重要因素。利用试探函数法导出了耗散非线性薛定谔方程的渐近解。在此基础上，讨论了耗散对包络孤立Rossby波演化的影响。结果表明，耗散使包络Rossby孤立波的振幅缓慢减小，宽度缓慢增加，但对传播速度没有影响。这与KdV型孤立波完全不同。值得注意的是，损耗对载波频率有一定的影响。
We solve the so‐called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt‐Vaisala frequency, andβeffect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV‐type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.