The Complete Solution of the Long‐Wave–Short‐Wave Resonance Equations

Abstract

We give a complete analysis of the long‐wave–short‐wave resonance equations which appear in fluid mechanics as well as plasma physics. Using the inverse‐scattering technique, these equations can be reduced to a pair of linear integral equations (Marchenko equations), with the N ‐soliton solutions intimately related to the asymptotic state of the evolution equations. The interaction of solitons and the conserved quantities are discussed.