New exact soliton solutions, bifurcation and multistability behaviors of
traveling waves for the (3+1)-dimensional modified Zakharov-Kuznetsov
equation with higher order dispersion
Abstract
The goal of the present paper is to obtain and analyze new exact
travelling wave solutions and bifurcation behavior of modified
Zakharov-Kuznetsov (mZK) equation with higher order dispersion term. For
this purpose, first and second simple methods are used to build soliton
solutions of travelling wave solutions. Furthermore, bifurcation
behavior of traveling waves including new type of quasiperiodic and
multi-periodic traveling wave motions have been examined depending on
the physical parameters. Multistability for the nonlinear mZK equation
has been investigated depending on fixed values of physical parameters
with various initial conditions. The suggested methods for the
analytical solutions are powerful and benefical tools to obtain the
exact travelling wave solutions of nonlinear evolution equations
(NLEEs). Two and three-dimensional plots are also provided to illustrate
the new solutions. Bifurcation and multistability behaviors of traveling
wave solution of the nonlinear mZK equation with higher order dispersion
will add some value in the literature of mathematical and plasma
physics.