Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation
Kai-Hua Yin1, Xue-Ping Cheng1,2*, and Ji Lin3
1School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, China 2Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhoushan 316022, China 3Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract：Starting from a general sixth-order nonlinear wave equation, we present its multiple kink solutions, which are related to the famous Hirota form. We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures. By introducing the velocity resonance mechanism to the multiple kink solutions, we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients. The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited. After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada–Kotera–Caudrey–Dodd–Gibbons (SKCDG) equation, the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.
2021, Vol. 38 
