Exact cross kink-wave solutions and resonance for the Jimbo–Miwa equation

Theta Function Solutions of the 3 + 1‐Dimensional Jimbo‐Miwa Equation

“…Authors presented rational solutions of (1) with the aid of the generalized Riccati equation mapping method [42]. By utilizing two-soliton method and bilinear method, cross kink-wave and periodic solitary solutions of (1) are given in [43]. With the help of the bilinear form, here we construct one-periodic and two-periodic solutions of this equation (1) by utilizing the method of Dai et al [19].…”

Cross-kink multi-soliton solutions for the (3+1)-D Jimbo-Miwa equation

“…In this paper, we consider the following Jimbo-Miwa [4]. By means of the two-soliton method and bilinear methods, the the two-soliton solutions, three-wave solutions of the Jimbo-Miwa were found as well as [5][6].…”

Multidromion Soliton and Rouge Wave for the (2 + 1)-Dimensional Broer-Kaup System with Variable Coefficients

“…Searching for explicit solutions of nonlinear evolution equations by using various different methods is useful and meaningful in physical science and nonlinear science. Many powerful methods have been presented, such as inverse scattering transform [1], Hirota's bilinear form method [2], two-soliton method [3], homoclinic test technique [4][5][6], the Bäcklund transformation method [7], three-wave type of ansätz approach [8,9], projective equation method [10], and multilinear variable separation method [11].…”