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D.E. Pelinovsky and R.H.J. Grimshaw

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Spectral transform for the intermediate nonlinear
Schrodinger equation

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J.Math.Phys. 36, 4203-4219 (1995)

**Abstract:**

A new spectral transform system is introduced to solve
the initial-value problem for the intermediate nonlinear
Schrodinger (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 Backlund-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.

**Keywords:**

INVERSE SCATTERING TRANSFORM, BENJAMIN-ONO EQUATION,
LONG-WAVE EQUATION, EVOLUTION EQUATIONS,
INTEGRABILITY, RESCALINGS