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Exact solutions with Jacobi elliptic functions of two nonlinear models for ion-acoustic plasma waves. (English) Zbl 1076.35099

Summary: The periodic wave solutions of two nonlinear models for ion-acoustic plasma waves, including the mixed Korteweg-de Vries (KdV) and modified KdV equation and the \((3+ 1)\)-dimensional modified Zakharov-Kuznetsov equation, are obtained by using the \(F\)-expansion method and introducing appropriate transformations. In the limiting cases, the solitary wave solutions of the equations are also obtained.

MSC:

35Q35 PDEs in connection with fluid mechanics
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
35C05 Solutions to PDEs in closed form
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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