A Dimensional Integrable Generalization of the Sine‐Gordon Equation I. ‐∂‐Dressing and the Initial Value Problem

Publisher: John Wiley & Sons Inc

E-ISSN: 1467-9590|90|3|189-223

ISSN: 0022-2526

Source: STUDIES IN APPLIED MATHEMATICS, Vol.90, Iss.3, 1993-12, pp. : 189-223

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Abstract

The 2+1 dimensional integrable generalization of the sine‐Gordon equation symmetric in the spatial variables is studied by the inverse spectral transform method. The solutions with functional parameters, plane solitons (kinks) and plane breathers are constructed by the dressing method based on the mixed nonlocal ‐∂‐problem. The initial value problem for this equation with the constant boundaries is solved in both cases σ2 = ± 1.