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Boundary value problems for the N-wave interaction equations

Pelloni, 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

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To link to this article DOI: 10.1016/j.physleta.2009.03.064

Abstract/Summary

We 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:7272
Publisher:Elsevier

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