A class of coupled nonlinear Schr&ouml;dinger equations: Painlev&acute;e property, exact solutions, and application to atmospheric gravity waves

LIU Ping;LI Zi-Liang;LOU Sen-Yue

doi:10.1007/s10483-010-1370-6

2010 , Vol. 31 >Issue 11: 1383 - 1404

DOI: https://doi.org/10.1007/s10483-010-1370-6

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A class of coupled nonlinear Schrödinger equations: Painlev´e property, exact solutions, and application to atmospheric gravity waves

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1. Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, Guangdong Province, P. R. China;
2. Department of Marine Meteorology, Ocean University of China, Qingdao 266100, Shandong Province, P. R. China;
3. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China; 4. Faculty of Science, Ningbo University, Ningbo 315211, Zhejiang Province, P. R. China

Received date: 2010-04-04

Revised date: 2010-09-30

Online published: 2010-11-01

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Abstract

The Painlev´e integrability and exact solutions to a coupled nonlinear Schrödinger (CNLS) equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painlev´e test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

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LIU Ping;LI Zi-Liang;LOU Sen-Yue . A class of coupled nonlinear Schrödinger equations: Painlev´e property, exact solutions, and application to atmospheric gravity waves[J]. Applied Mathematics and Mechanics, 2010 , 31(11) : 1383 -1404 . DOI: 10.1007/s10483-010-1370-6

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