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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

35Q99PDE of mathematical physics and other areas
35P25Scattering theory (PDE)
35R30Inverse problems for PDE
35L75Nonlinear hyperbolic PDE of higher $(>2)$ order
35A30Geometric theory for PDE, characteristics, transformations