Solution of the Dirichlet boundary value problem for the Sine-Gordon equation
نویسنده
چکیده
The sine-Gordon equation in light cone coordinates is solved when Dirichlet conditions on the L-shape boundaries of the strip {t ∈ [0, T ]} ∪ {x ∈ [0,∞]} are prescribed in a class of functions that vanish (mod 2π) as x → ∞ at initial time. The method is based on the inverse spectral transform (IST) for the Schrödinger spectral problem on the semi-line x > 0 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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