Riemann-Hilbert approach for the FQXL model: A generalized Camassa-Holm equation with cubic and quadratic nonlinearity

Authors

Zhen Wang, Dalian University of Technology
Zhijun Qiao, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

7-27-2016

Abstract

In this paper, the inverse scattering transform associated with a Riemann-Hilbert problem is formulated for the FQXL model: a generalized Camassa-Holm equation mt = 12 k1[m(u2 − u2 x )]x + 1 2 k2(2mux + mxu), m = u − ux x, 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.

Comments

Published by AIP Publishing. Original published version available at https://doi.org/10.1063/1.4959232

Recommended Citation

Wang, Zhen, and Zhijun Qiao. 2016. “Riemann-Hilbert Approach for the FQXL Model: A Generalized Camassa-Holm Equation with Cubic and Quadratic Nonlinearity.” Journal of Mathematical Physics 57 (7): 073505. https://doi.org/10.1063/1.4959232.

Publication Title

Journal of Mathematical Physics

DOI

10.1063/1.4959232