A class of coupled nonlinear Schr(o)dinger equations: Painlevé property,exact solutions,and application to atmospheric gravity waves

摘要

The Painlev'e integrability and exact solutions to a coupled nonlinear Schr¨odinger (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.