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Bäcklund Transformations and Inverse Scattering Solutions for Some Pseudospherical Surface Equations
Author(s) -
Beals Richard,
Rabelo Mauro,
Tenenblat Keti
Publication year - 1989
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 - 10.1002/sapm1989812125
Subject(s) - mathematics , inverse , surface (topology) , mathematical analysis , inverse scattering problem , mathematical physics , scattering , inverse problem , geometry , physics , quantum mechanics
In is known that the equations [ u t − g ( u ) u x ] x = ± g′ ( u ) describe pseudo‐spherical surfaces, i.e. that these equations are the integrability conditions for the structural equations of such surfaces, provided g satisfies g′ + µg = θ . In this paper we obtain self‐Bäcklund transformations for these equations by a geometric method, and show how the inverse scattering method generates global solutions.