In this article,the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method,hyperbolic secant expansion method,and Jacobi elliptic function expansion method.They obtain more exact traveling wave solutions including trigonometric function solutions,rational function solutions,and more generally solitary waves,which are called classical bright soliton,W-shaped soliton,and M-shaped soliton.
Zakharov equations have a fairly abundant physical background. In this paper, the existence of the weak global solution for quantum Zakharov equations for the plasmas model is obtained by means of the Arzela-Ascoli theorem, Faedo-Galerkin methods, and compactness property.
A class of periodic initial value problems for two-dimensional Newton-Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.
