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Maximal amplitudes of hyperelliptic solutions of the derivative nonlinear Schrödinger equation
Author(s) -
Wright Otis C.
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12299
Subject(s) - upper and lower bounds , mathematics , nonlinear system , amplitude , mathematical analysis , bound state , nonlinear schrödinger equation , mathematical physics , derivative (finance) , simple (philosophy) , schrödinger equation , physics , quantum mechanics , philosophy , epistemology , financial economics , economics
A simple formula is proven for an upper bound for amplitudes of hyperelliptic (finite‐gap or N ‐phase) solutions of the derivative nonlinear Schrödinger equation. The upper bound is sharp, viz, it is attained for some initial conditions. The method used to prove the upper bound is the same method, with necessary modifications, used to prove the corresponding bound for solutions of the focusing NLS equation (Wright OC, III. Sharp upper bound for amplitudes of hyperelliptic solutions of the focusing nonlinear Schrödinger equation. Nonlinearity . 2019;32:1929‐1966).