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On the solution of the generalized wave and generalized sine-Gordon equations. (English) Zbl 0626.35082

The direct and inverse scattering problems associated with the n- dimensional generalized wave equation (GWE) and the generalized sine Gordon equation (GSGE) have been solved for initially prescribed data along certain lines. The methodology involves reduction of the n- dimensional equation into a coupled system of n linear one-dimensional ordinary differential equations which could in turn be subject to detailed scattering analysis. The linear scattering problem is more amenable particularly to equations in more than three independent variables for which generally one has to consider scattering data which satisfy nonlinear equations. The present analysis avoids this constraint.
Reviewer: P.Chandran

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
35L75 Higher-order nonlinear hyperbolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
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