An integrable generalization of the sine-Gordon equation on the half-line

2009/11/04 by Jonatan Lenells, Lenells, Jonatan
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.0911.0848

18 pages, 5 figures; some minor corrections

arxiv created 2010/11/12 · arxiv updated 2010/11/15

Abstract

We analyze a generalization of the sine-Gordon equation in laboratory coordinates on the half-line. Using the Fokas transform method for the analysis of initial-boundary value problems for integrable PDEs, we show that the solution u(x,t) can be constructed from the initial and boundary values via the solution of a 2× 2-matrix Riemann-Hilbert problem.

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