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

2016/01/05 by Marco Bertola, Bertola, Marco, Alexander Tovbis +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1601.00875

22 pages, 2 figures

arxiv created 2016/01/05 · openalex publication_date 2016/01/05 · arxiv updated 2016/01/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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