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On the Solution of the Generalized Wave and Generalized Sine‐Gordon Equations
Author(s) -
Ablowitz Mark J.,
Beals Richard,
Tenenblat Keti
Publication year - 1986
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/sapm1986743177
Subject(s) - mathematics , mathematical analysis , boundary value problem , sine , sine gordon equation , differential equation , initial value problem , partial differential equation , independent equation , wave equation , nonlinear system , physics , soliton , geometry , quantum mechanics
The generalized wave equation and generalized sine‐Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two‐dimensional versions. In this paper we associate a system of linear differential equations with these equations and show how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial‐boundary‐value problem is solved for these equations.