A spectral transform for the intermediate nonlinear Schrödinger equation

A new spectral transform system is introduced to solve the initial-value problem for the intermediate nonlinear Schrödinger (INLS) equation describing envelope waves in a deep stratified fluid. The spectral system is a combination of the Zakharov–Shabat linear system and a local Riemann–Hilbert problem in a strip of the complex plane. The inverse scattering transform technique is developed and the Bäcklund–Darboux transformation, soliton solutions and an infinite number of conservation laws are constructed. It is shown that all these properties of the INLS equation are closely related to those of the intermediate long-wave equation.