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Exact solutions of space–time dependent non‐linear Schrödinger equations
Author(s) -
Ruan Hangyu,
Li Huijun,
Chen Yixin
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.486
Subject(s) - mathematics , transformation (genetics) , mathematical analysis , dispersion (optics) , schrödinger equation , space (punctuation) , quantum mechanics , physics , biochemistry , chemistry , linguistics , philosophy , gene
Abstract Using a general symmetry approach we establish transformations between different non‐linear space–time dependent evolution equations of Schrödinger type and their respective solutions. As a special case we study the transformation of the standard non‐linear Schrödinger equation (NLS)‐equation to a NLS‐equation with a dispersion coefficient which decreases exponentially with increasing distance along the fiber. By this transformation we construct from well known solutions of the standard NLS‐equation some new exact solutions of the NLS‐equation with dispersion. Copyright 2004 John Wiley & Sons, Ltd.