## Abstract and Applied Analysis

### Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution

#### Abstract

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, and $\beta$ effect 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 643652, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412607178

Digital Object Identifier
doi:10.1155/2014/643652

Mathematical Reviews number (MathSciNet)
MR3253582

Zentralblatt MATH identifier
07022813

#### Citation

Shi, Yunlong; Yin, Baoshu; Yang, Hongwei; Yang, Dezhou; Xu, Zhenhua. Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 643652, 9 pages. doi:10.1155/2014/643652. https://projecteuclid.org/euclid.aaa/1412607178

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