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Zbl 0626.35082
Ablowitz, Mark J.; Beals, Richard; Tenenblat, Keti
On the solution of the generalized wave and generalized sine-Gordon equations. (English)
[J] Stud. Appl. Math. 74, 177-203 (1986). ISSN 0022-2526; ISSN 1467-9590/e

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.
[P.Chandran]

MSC 2000:: *35Q99 PDE of mathematical physics and other areas
35P25 Scattering theory (PDE)
35R30 Inverse problems for PDE
35L75 Nonlinear hyperbolic PDE of higher $(>2)$ order
35A30 Geometric theory for PDE, transformations

Keywords: inverse scattering transform; diffeomorphism; Bäcklund transformation; hyperbolic manifold; compatibility conditions; generalized wave equation; generalized sine Gordon equation

Cited in: Zbl 0646.35058

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