| Variational iteration method is a concise and effective approximate method for solving nonlinear differential equations.It is suitable for many differential equation solving problems with practical background.Nonlinear problems are very important in many scientific fields.Therefore,it is particularly important to find the exact solution or analytical approximate solution of nonlinear equations.Variational iteration method can effectively find the analytical approximate solution of nonlinear equations.Zakharov-Kuznestov(Z-K)equation is an important nonlinear wave equation obtained by extending Korteweg-de Vries(KdV)equation in two-dimensional space.It describes the evolution process of plane wave in magnetized plasma and has important theoretical significance and application value for the study of nonlinear wave phenomena.Due to the different parameters in the equation,the equation can be divided into linear equation and nonlinear equation.At present,variational iteration method has been recognized as one of the effective solutions to nonlinear problems,which is more flexible and widely used.Its advantage is that it does not need linearization,and only needs iteration to obtain an analytical approximate solution with high accuracy.In this paper,the variational iterative method is applied to solve the Z-K equation.According to the different coefficients,the variational iterative formulas are established for one-dimensional and two-dimensional problems respectively.By introducing the definition of restricted variational,the multiplier in the iterative formula is obtained.Further select the appropriate initial function and construct a relatively simple variational iterative formula.After multiple iterations,the exact solution(linear problem)and analytical approximate solution(nonlinear problem)of the corresponding Z-K equation are obtained,and the numerical simulation calculation is carried out. |
