Multiple-mode wave solutions to display superpositions and collisions in nonlinear evolution equations.
We present a general method for obtaining multiple-mode waves (MMWs), which is introduced as a concept expressed in the form of nonlinear superpositions of single-mode waves (SMWs) with different wave speeds, for nonlinear evolution equations. The validity of the approach has been demonstrated using two wave equations. It is shown that MMWs may combine different types of SMWs such as periodic waves, kink waves, compactons, solitary waves, etc., to form more general solutions, which can be used to display the whole evolution process of interactions between different types of waves, especially to reveal the dynamic details of the wave patterns.
Faculty of Science, Jiangsu University, Zhenjiang, China. qbi@ujs.edu.cn
Qinsheng
Q
Bi
Zhengdi
Z
Zhang