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Quasiperiodie Solutions of the Nonlinear Schrödinger Equation
Author(s) -
Mertsching J.
Publication year - 1987
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190350704
Subject(s) - quasiperiodic function , riemann hypothesis , soliton , mathematics , simple (philosophy) , nonlinear schrödinger equation , nonlinear system , schrödinger's cat , mathematical physics , spectral theory , mathematical analysis , schrödinger equation , physics , quantum mechanics , philosophy , epistemology , hilbert space
Using an elementary version of the inverse spectral theory, a review of quasiperiodic solutions of the (1 + 1) dimensional eubic Schrödinger equation in terms of Riemann's theta functions is given. The general theory is illustrated by simple examples. In particular, the kink and soliton limits, and their relations to Bäcklund transformations are discussed.