Variational Principles and Solitary Wave Solutions of Generalized Nonlinear Schrödinger Equation in the Ocean

Abstract

Internal solitary waves are very common physical phenomena in the ocean, which play an important role in the transport of marine matter, momentum and energy. Because the generalized nonlinear Schrodinger equation can well explain the effects of nonlinearity and dispersion in the ocean, it is more suitable for describing the deep-sea internal wave propagation and evolution than other mathematical models. At first, by designing skillfully the trial-Lagrange functional, different kinds of variational principles are successfully established for a generalized nonlinear Schrodinger equation by the semi-inverse method. Then, the constructed variational principles are proved correct by minimizing the functionals with the calculus of variations. Furthermore, some kinds of internal solitary wave solutions are obtained and demonstrated by semi-inverse variational principle for the generalized nonlinear Schrodinger equation.