Solution of the Dirichlet boundary value problem for the Sine-Gordon equation

Details Solution of the Dirichlet boundary value problem for the Sine-Gordon equation Solution of the Dirichlet boundary value problem for the Sine-Gordon equation

2002-04-17

arxiv.org/abs/nlin/0204042v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex file, to appear in Physics Letters A

Scientific paper

10.1016/S0375-9601(02)00514-5

The sine-Gordon equation in light cone coordinates is solved when Dirichlet conditions on the L-shape boundaries of the strip [0,T]X[0,infinity) are prescribed in a class of functions that vanish (mod 2 pi) for large x at initial time. The method is based on the inverse spectral transform (IST) for the Schroedinger spectral problem on the semi-line solved as a Hilbert boundary value problem. Contrarily to what occurs when using the Zakharov-Shabat eigenvalue problem, the spectral transform is regular and in particular the discrete spectrum contains a finite number of eigenvalues (and no accumulation point).

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