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Z. Naturforsch. 69a, 239 – 248
(2014)
doi:10.5560/ZNA.2014-0018
Multi-Soliton Solutions and Interaction for a Generalized Variable-Coefficient Calogero–Bogoyavlenskii–Schiff Equation
Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Received December 13, 2013 / revised March 9, 2014 / published online May 21, 2014
Reprint requests to: Y.-T. G.; E-mail:
gaoyt@public.bta.net.cn
In this paper, a generalized variable-coefficient Calogero–Bogoyavlenskii–Schiff equation is investigated. Based on the Bell polynomials and an auxiliary variable, bilinear forms of such an equation are obtained. One-, two-, and three-soliton solutions are given through the Hirota method and symbolic computation. N-soliton solutions are also constructed. Multi-soliton interaction and propagation are investigated and illustrated: (i) properties of the multi-soliton interaction on different planes in space depend on the forms of the only variable coefficient; (ii) positions of the solitons change when the wave numbers have the reverse signs.
Key words: Generalized Variable-Coefficient Calogero–Bogoyavlenskii–Schiff Equation; Bell Polynomials; Bilinear Form; N-Soliton Solutions.
PACS numbers: 05. 45. Yv; 47. 35. Fg; 02. 30. Jr