Integrable evolution equations in time-dependent domains
Fokas, A. S. and Pelloni, B. (2001) Integrable evolution equations in time-dependent domains. Inverse Problems, 17 (4). pp. 919-935. ISSN 0266-5611
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To link to this article DOI: 10.1088/0266-5611/17/4/323
We discuss the implementation of a method of solving initial boundary value problems in the case of integrable evolution equations in a time-dependent domain. This method is applied to a dispersive linear evolution equation with spatial derivatives of arbitrary order and to the defocusing nonlinear Schrödinger equation, in the domain l(t)<x<∞, 0<t<T, where l(t) is a given real sufficiently smooth function whose first derivative is monotonic, and T is a fixed positive constant.