Author(s)

Hanxi Wei

Corresponding Author

Hanxi Wei

Abstract

This study investigates the long-wave dynamics of interfacial waves in a two-layer incompressible, inviscid fluid system. Starting from the full potential formulation, we employ a Dirichlet–Neumann operator approach to derive a new class of nonlinear evolution equations, thereby avoiding the direct solution of Laplace’s equation. By performing asymptotic expansions of the Dirichlet–Neumann operator under various long-wave scaling, we obtain a hierarchy of reduced models—including the Korteweg–de Vries (KdV), fifth-order KdV, modified KdV (mKdV), and Benjamin equations. This approach significantly reduces computational complexity while retaining key nonlinear and dispersive effects, and provides a unified and efficient framework for modelling interfacial wave propagation in stratified fluids.

Keywords

Dirichlet-Neumann Operator; Asymptotic Analysis; Nonlinear Waves; Interfacial Waves