Boundary value problems for the N-wave interaction equationsPelloni, B. and Pinotsis, D. (2009) Boundary value problems for the N-wave interaction equations. Physics Letters A, 373 (22). pp. 1940-1950. ISSN 0375-9601 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.physleta.2009.03.064 Abstract/SummaryWe consider boundary value problems for the N-wave interaction equations in one and two space dimensions, posed for x [greater-or-equal, slanted] 0 and x,y [greater-or-equal, slanted] 0, respectively. Following the recent work of Fokas, we develop an inverse scattering formalism to solve these problems by considering the simultaneous spectral analysis of the two ordinary differential equations in the associated Lax pair. The solution of the boundary value problems is obtained through the solution of a local Riemann–Hilbert problem in the one-dimensional case, and a nonlocal Riemann–Hilbert problem in the two-dimensional case.
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