Interactions between solitons and other nonlinear Schrödinger waves.
The nonlinear Schrödinger (NLS) equation is widely used in natural science. Various nonlinear excitations of the NLS equation have been found by many methods. However, except for the soliton-soliton interactions, it is very difficult to find interaction solutions between different types of nonlinear excitations. In this paper, the symmetry reduction method is further developed to find interaction solutions between solitons and other types of NLS waves. Especially, the soliton-cnoidal wave interaction solutions are explicitly studied in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integrals. Some special concrete interaction solutions and their asymptotic behaviors are discussed both in analytical and graphical ways.
Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China.
Xue-Ping
XP
Cheng
Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China and Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China and Faculty of Science, Ningbo University, Ningbo, 315211, China.
S Y
SY
Lou
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China.
Chun-Li
CL
Chen
Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China.
Xiao-Yan
XY
Tang