Internal solitary waves in the ocean by semi-inverse variational principle

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. The non-linear Schrodinger equation is suitable for describing the deep-sea internal wave propagation. Firstly, by designing skillfully, the trial-Lagrange functional, variational principles are successfully established for the non-linear Schrodinger equation by the semi-inverse method. Secondly, the constructed var-iational principle is proved by minimizing the functionals with the calculus of variations. Finally, different kinds of internal solitary waves are obtained by the semi-inverse variational principle for the non-linear Schrodinger equation.