College of Science, Henan University of Engineering, 451191, Zhengzhou, China
Abstract:
Under investigation in this paper is a $(3+1)$-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV–ZK) equation, which describes the nonlinear behaviors of ion-acoustic waves in a magnetized plasma where the cooler ions are treated as a fluid with adiabatic pressure and the hot isothermal electrons are described by a Boltzmann distribution. With the Homotopy analysis method and symbolic computation, we obtain its periodic approximate solutions expressed by the Fourier series. The solutions contains an extra auxiliary parameter $h$, which provide us with a simple way to adjust and control the convergence region of solution series. In order to overcome the shortage of convergence rate and improve the accuracy of homotopy-series solution, we introduce the $M$th-order homotopy-iteration approach, which greatly accelerates the approximation rate and improves the approximation results. The results we derived, in this article, are useful to study and verify the analytical solutions with numerical and experimental solutions in plasma physics.
Key words:mKdV–ZK equation, homotopy analysis method, analytic solution, series solutions.
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