Existence of Solitary Internal Waves in a Two-Layer Fluid of Infinite Height

摘要

This paper concerns the existence of internal solitary waves moving with aconstant speed at the interface of a two-layer fluid with infinite height. The fluids are immiscible, inviscid, and incompressible with constant but different densities. Assume that the height of the upper fluid is infinite and the depth of the lower fluid is finite. It has been formally derived before that under long-wave assumption the first-order approximation of the interface satisfies the Benjamin-Ono equation, which has algebraic solitary-wave solutions. This paper gives a rigorous proof of the existence of solitary-wave solutions of the exact equations governing the fluid motion, whose first-order approximations are the algebraic solitary-wave solutions of the Benjamin-Ono equation. The proof relies