具有幂律非线性的(3 + 1)维Zakharov-Kuznetsov方程的行波解

Traveling Wave Solutions of the (3 + 1)-Dimensional Zakharov-Kuznetsov Equation with Power Law Nonlinearity

本文应用动力系统分岔理论研究了具有幂律非线性的(3 + 1)维Zakharov-Kuznetsov方程的行波。通过将Zakharov-Kuznetsov方程的行波系统转化为R2中的动力学系统,得到了保证其有界和无界轨道存在的各种参数条件。此外,通过计算这些轨道上的复杂椭圆积分,我们得到了(3 + 1)维Zakharov-Kuznetsov方程n = 1的所有可能行波解的精确表达式。

In this paper, the bifurcation theory of dynamical system is applied to study the traveling waves of the (3 + 1)-dimensional Zakharov-Kuznetsov equation with power law nonlinearity. By transforming the traveling wave system of the Zakharov-Kuznetsov equation into a dynamical system in R2, we derive various parameter conditions that guarantee the existence of its bounded and unbounded orbits. Furthermore, by calculating complicated elliptic integrals along these orbits, we obtain exact expressions of all possible traveling wave solutions of the (3 + 1)-dimensional Zakharov-Kuznetsov equation for n = 1.