Boundary value problems for the N-wave interaction equations

Beatrice Pelloni; Dimitrios Pinotsis

doi:10.1016/j.physleta.2009.03.064

Boundary value problems for the N-wave interaction equations

Beatrice Pelloni, Dimitrios Pinotsis

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider boundary value problems for the N -wave interaction equations in one and two space dimensions, posed for x⩾0 and x,y⩾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.

Original language	English
Pages (from-to)	1940-1950
Number of pages	11
Journal	Physics Letters A
Volume	373
Issue number	22
DOIs	https://doi.org/10.1016/j.physleta.2009.03.064
Publication status	Published - 11 May 2009

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10.1016/j.physleta.2009.03.064

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title = "Boundary value problems for the N-wave interaction equations",

abstract = "We consider boundary value problems for the N -wave interaction equations in one and two space dimensions, posed for x⩾0 and x,y⩾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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N2 - We consider boundary value problems for the N -wave interaction equations in one and two space dimensions, posed for x⩾0 and x,y⩾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.

AB - We consider boundary value problems for the N -wave interaction equations in one and two space dimensions, posed for x⩾0 and x,y⩾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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VL - 373

SP - 1940

EP - 1950

JO - Physics Letters A

JF - Physics Letters A

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Boundary value problems for the N-wave interaction equations

Abstract

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