Riemann-Hilbert approach for the FQXL model: A generalized Camassa-Holm equation with cubic and quadratic nonlinearity.
In: Journal of Mathematical Physics, Jg. 57 (2016-07-01), Heft 7, S. 1-18
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Zugriff:
In this paper, the inverse scattering transform associated with a Riemann-Hilbert problem is formulated for the FQXL model: a generalized Camassa-Holm equation m t = ½k 1 [m(u² - u² x )] x + ½k 2 (2mu x + m x u), m = u - u xx , which was originally included in the work of Fokas [Physica D 87, 145 (1995)] and was recently shown to be integrable in the sense of Lax pair, bi-Hamilton structure, and conservation laws by Qiao, Xia, and Li [e-print arXiv:1205.2028v2 (2012)]. We have discussed the following properties: direct scattering problems and Jost solutions, asymptotical and analytical behavior of Jost solutions, the scattering equations in a Riemann-Hilbert problem, and the multi-soliton solutions of the FQXL model. Then, one-soliton and two-soliton solutions are presented in a parametric form as a special case of multi-soliton solutions. [ABSTRACT FROM AUTHOR]
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Titel: |
Riemann-Hilbert approach for the FQXL model: A generalized Camassa-Holm equation with cubic and quadratic nonlinearity.
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Autor/in / Beteiligte Person: | Wang, Zhen ; Qiao, Zhijun |
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Zeitschrift: | Journal of Mathematical Physics, Jg. 57 (2016-07-01), Heft 7, S. 1-18 |
Veröffentlichung: | 2016 |
Medientyp: | academicJournal |
ISSN: | 0022-2488 (print) |
DOI: | 10.1063/1.4959232 |
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