Group Analysis of Nonlinear Internal Waves in Oceans. I:   Self-adjointness, conservation laws, invariant solutions
  The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint.   This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams. 
Nail H. Ibragimov and Ranis N. Ibragimov
math-ph math.MP