Abstract
The generalized Zakharov equation is a coupled equation which is a classic nonlinear mathematic model in plasma. A series of new exact explicit solutions of the system are obtained, by means of the first integral method, in the form of trigonometric and exponential functions. The results show the first integral method is an efficient way to solve the coupled nonlinear equations and get rich explicit analytical solutions.
Highlights
The generalized Zakharov equation have been the focus of many researchers due to two facts: the system is a classic nonlinear mathematic model in plasma physics; the exact solutions to the system are widely applied in many scientific and engineering fields
We discussed how to construct the exact solutions for the generalized Zakharov equation by using the first integral method
Many new exact explicit solutions with arbitrary constant, peaked wave solutions are obtained, they may be important for the explanation of some practical physical problems
Summary
The generalized Zakharov equation have been the focus of many researchers due to two facts: the system is a classic nonlinear mathematic model in plasma physics; the exact solutions to the system are widely applied in many scientific and engineering fields. How to cite this paper: Sun, Y.H., et al (2014) New Exact Explicit Solutions of the Generalized Zakharov Equation via the First Integral Method. Bin Lu applied this method to construct travelling wave solutions of the (2 + 1)-dimensional BKK system and (3 + 1)-dimensional Burgers equation [12], Hodsein et al reported new solutions of the Davey-Stewartson equation by using this method [13], the method has been successfully adopted for solving some important complex partial differential equations in [14]-[23]. In order to explore new analysis solutions to the system (1), we attempted to use the first integral method to solve the generalized Zakharov equation for the first time.
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