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Abstract and Applied Analysis
Volume 2014, Article ID 643652, 9 pages
http://dx.doi.org/10.1155/2014/643652
Research Article

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

1Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China
4College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Received 3 July 2014; Accepted 9 August 2014; Published 19 August 2014

Academic Editor: Huanhe Dong

Copyright © 2014 Yunlong Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 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.