Rogue waves on the double-periodic background in the focusing nonlinear Schrodinger equation

TL;DR

This paper constructs double-periodic solutions to the focusing nonlinear Schrödinger equation using an algebraic method, characterizes their spectra, and analyzes rogue waves that emerge on these backgrounds, including numerical magnification studies.

Contribution

It introduces an algebraic approach with two eigenvalues for constructing double-periodic solutions and characterizes the associated Lax spectrum.

Findings

Characterization of the Lax spectrum for double-periodic solutions

Construction of rogue waves on double-periodic backgrounds

Numerical analysis of rogue wave magnification

Abstract

The double-periodic solutions of the focusing nonlinear Schrodinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues. Furthermore, we characterize the Lax spectrum for the double-periodic solutions and analyze rogue waves arising on their background. Magnification of the rogue waves is studied numerically.