Yaning Tang

Hirota bilinear equations with linear subspaces of solutions

We explore when Hirota bilinear equations possess linear subspaces of solutions. First, we establish a sufficient and necessary criterion for the existence of linear subspaces of exponential traveling wave solutions to Hirota bilinear equations. Second, we show that multivariate polynomials whose zeros form a vector space can generate the desired Hirota bilinear equations with given linear subspaces of solutions, and formulate such multivariate polynomials by using multivariate polynomials which have one and only one zero. Third, applying an algorithm using weights, we present parameterizations of wave numbers and frequencies achieved by using one parameter to compute the desired Hirota bilinear equations.

Travelling wave solutions for modified Zakharov–Kuznetsov equation

Abstract By using the theory of bifurcations of dynamical systems to the modified Zakharov–Kuznetsov equation which describes wave propagation in isothermal multicomponent magnetized plasmas, numbers of solitary waves and periodic waves and kink waves are obtained. Under various parameter conditions, all explicit formulas of solitary waves solutions, periodic waves solutions and kink waves solutions are given.

Binary Bell polynomials, Hirota bilinear approach to Levi equation

Combining the binary Bell polynomials and Hirota method, we obtained two kinds of equivalent bilinear equations for the Levi equation. Then, we got the double Wronskian solutions of the Levi equation by virtue of one of the bilinear equations. Furthermore, we constructed the bilinear Backlund transformation and the Lax pair. Finally, we also derived the Darboux transformation and the infinite conservation laws of the Levi equation.