Evolution of initial discontinuities in the DNLS equation theory

TL;DR

This paper classifies wave patterns from initial discontinuities in the DNLS equation, revealing complex structures and new wave types, with applications in fiber optics and Alfvén wave phenomena.

Contribution

It provides a comprehensive classification of wave evolutions in the DNLS equation for arbitrary boundary conditions, introducing new wave structures and extending dispersive hydrodynamics theory.

Findings

Classification of wave patterns from initial discontinuities.

Identification of new simple-wave-like structures.

Application potential in fiber optics and plasma physics.

Abstract

We present the full classification of wave patterns evolving from an initial step-like discontinuity for arbitrary choice of boundary conditions at the discontinuity location in the DNLS equation theory. In this non-convex dispersive hydrodynamics problem, solutions of the Whitham modulation equations are mapped to parameters of a modulated wave by two-valued functions what makes situation much richer than that for a convex case of the NLS equation type. In particular, new types of simple-wave-like structures appear as building elements of the whole wave pattern. The developed here theory can find applications to propagation of light pulses in fibers and to the theory of Alfv\'en dispersive shock waves.