The triple Wronskian solutions to the variable-coefficient Manakov model

In this paper, the variable-coefficient Manakov model whose bilinear form exists is mainly discussed. Based on the Wronskian technique, the triple Wronskian form solutions are obtained and the interactions between the two solitons are investigated.

New Exact Solutions for the (3+1)-Dimensional Generalized BKP Equation

The Wronskian technique is used to investigate a (3+1)-dimensional generalized BKP equation. Based on Hirota’s bilinear form, new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions are formally derived. Moreover we analyze the strangely mechanical behavior of the Wronskian determinant solutions. The study of these solutions will enrich the variety of the dynamics of the nonlinear evolution equations.

The Wronskian Solution and Soliton Resonance of the Nonisospectral Generalised Sawada–Kotera Equation

The bilinear form of the nonisospectral generalized Sawada–Kotera equation is derived. With the aid of the Wronskian technique, the Wronskian solution is presented for this equation. The soliton resonance is discussed in inhomogeneous media. Negatons and positons are also obtained.

Two Different Classes of Wronskian Conditions to a (3 + 1)-Dimensional Generalized Shallow Water Equation

Based on the Hirota bilinear method and Wronskian technique, two different classes of sufficient conditions consisting of linear partial differential equations system are presented, which guarantee that the Wronskian determinant is a solution to the corresponding Hirota bilinear equation of a (3+1)-dimensional generalized shallow water equation. Our results show that the nonlinear equation possesses rich and diverse exact solutions such as rational solutions, solitons, negatons, and positons.

N-SOLITON-LIKE SOLUTIONS AND BÄCKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION

A non-isospectral and variable-coefficient modified Korteweg–de Vries (mKdV) equation is investigated in this paper. Starting from the Ablowitz–Kaup–Newell–Segur procedure, the Lax pair is established and the Bäcklund transformation in original variables is also derived. By a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. In addition, the bilinear Bäcklund transformation gives a one-soliton-like solution from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique.

Double Wronskian Solution and Conservation Laws for a Generalized Variable-Coefficient Higher-Order Nonlinear Schrödinger Equation in Optical Fibers

With applications in the higher-power and femtosecond optical transmission regime, a generalized variable-coefficient higher-order nonlinear Schrödinger (VC-HNLS) equation is analytically investigated. The multi-solitonic solutions of the generalized VC-HNLS equation in double Wronskian form is constructed and further verified using the Wronskian technique. Additionally, an infinite number of conservation laws for such an equation are presented. Finally, discussions and conclusions on results are made with figures plotted.