A Computational Method for Solitary Internal Waves in a Continuously Stratified Fluid

An iterative algorithm is presented to compute steady, translational nonlinear waves in an incompressible fluid with a stable density stratification. The method yields solitary internal waves as exact solutions of the governing Euler equations without the restrictions on wave amplitude or density profile involved in the various approximate models of weakly nonlinear long waves. Computed examples of large‐amplitude solutions in shallow and deep fluid regimes are given. A natural variational principle derived from the structure of the underlying dynamical equations forms the basis of the method. The construction of the numerical algorithm and the analysis of the properties of solutions are both developed from the same principle.