Maximum amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation

Abstract

In this paper we prove that the maximum amplitude of a finite-gap solution to the focusing Nonlinear Schrödinger equation with given spectral bands does not exceed half of the sum of the length of all the bands. This maximum will be attained for certain choices of the initial phases. A similar result is also true for the defocusing Nonlinear Schrödinger equation.

arXiv comment22 pages, 2 figures

Cited by in corpus (2)

• Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background
• On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight