The discrete mKdV equation revisited: a Riemann-Hilbert approach

2013/10/07 by Junyi Zhu, Xianguo Geng, Zhu, Junyi +3
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.1310.1666

19pages

arxiv created 2014/02/11 · arxiv updated 2014/02/13

Abstract

We study the plus and minus type discrete mKdV equation. Some different symmetry conditions associated with two Lax pairs are introduced to derive the matrix Riemann-Hilbert problem with zero. By virtue of regularization of the Riemann-Hilbert problem, we obtain the complex and real solution to the plus type discrete mKdV equation respectively. Under the gauge transformation between the plus and minus type, the solutions of minus type can be obtained in terms of the given plus ones.

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