Conservation Laws,Hamiltonian Structure,Modulational Instability Properties and Solitary Wave Solutions for a Higher‐Order Model Describing Nonlinear Internal Waves

Recent theoretical advances in connecting the wave‐induced mean flow with the conserved pseudomomentum per unit mass has permitted the first rational derivation of a model that describes the weakly nonlinear propagation of internal gravity plane waves in a continuously stratified fluid. Depending on the particular parameter regime examined the new model corresponds to an extended bright or dark derivative nonlinear Schrödinger equation or an extended complex‐valued modified Korteweg‐de Vries or Sasa–Satsuma equation. Mass, momentum, and energy conservation laws are derived. A noncanonical infinite‐dimensional Hamiltonian formulation of the model is introduced. The modulational stability characteristics associated with the Stokes wave solution of the model are described. The bright and dark solitary wave solutions of the model are obtained.