Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

• Published in: Communications in theoretical physics 2011-03, Vol.55 (3), p.473-480, Article 473
• Main Authors: Gai, Xiao-Ling (晓玲 盖), Gao, Yi-Tian (以天 高), Yu, Xin (鑫于), Sun, Zhi-Yuan (志远 孙), Wang, Lei (雷王)
• Format: Article
• Language: English
• Subjects: Collisions; Computational fluid dynamics; Dependent variables; KdV方程; Mathematical analysis; Mathematical models; Plasmas; Solitons; Transformations; 双孤子解; 弹性碰撞; 方程组; 相互作用; 非线性现象
• ISSN: 0253-6102
• DOI: 10.1088/0253-6102/55/3/20

Kortweg-de Vries （KdV）-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV （GCCKdV） equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented： （i） two solitons merge and separate from each other periodically; （ii） two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; （iii） two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing.