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Method for Solving the Sine‐Gordon Equation in Laboratory Coordinates
Author(s) -
Kaup D. J.
Publication year - 1975
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/sapm1975542165
Subject(s) - inverse scattering transform , inverse scattering problem , eigenvalues and eigenvectors , sine , inverse problem , sine gordon equation , mathematics , mathematical analysis , initial value problem , inverse , scattering , simple (philosophy) , scattering theory , physics , geometry , nonlinear system , optics , soliton , philosophy , epistemology , quantum mechanics
By solving the direct and inverse scattering problems for a rather ‘unconventional’ eigenvalue problem, we can solve the initial value problem for the sine‐Gordon equation entirely in laboratory coordinates. This allows us to extend and accurately define the class of initial value problems which can be solved by ‘inverse scattering transforms.’ Simple examples are given to illustrate both the direct and the inverse scattering methods.