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Intrinsic Geometry of the NLS Equation and Its Auto‐Bäcklund Transformation
Author(s) -
Rogers C.,
Schief W. K.
Publication year - 1998
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 - 10.1111/1467-9590.00093
Subject(s) - congruence (geometry) , mathematics , transformation (genetics) , nonlinear system , mathematical analysis , nonlinear schrödinger equation , context (archaeology) , representation (politics) , mathematical physics , classical mechanics , geometry , schrödinger equation , physics , quantum mechanics , paleontology , biochemistry , chemistry , biology , politics , political science , law , gene
The nonlinear Schrödinger equation is derived in a general intrinsic geometric setting involving a normal congruence originally investigated by Marris and Passman in 1969 in a hydrodynamical context. Geometric properties of members of the normal congruence are adduced and an intrinsic representation of the auto‐Bäcklund transformation is obtained for the nonlinear Schrödinger equation.