The modied Zakharov–Kuznetsov (mZK) equation, ut + uux + uxxx + uxyy = 0, (1) represents an anisotropic two-dimensional generalization of the Korteweg–de Vries equation and can be derived in a magnetized plasma for small amplitude Alfvén waves at a critical angle to the undisturbed magnetic field, and has been studied by many authors because of its importance [1–5]. However, Eq. (1) possesses m...

In this article, we prove that the ⟨p,q⟩ condition holds, first by using Fuchs index of complex Kawahara equation, and then proving all meromorphic solutions equations belong to class W. Moreover, method is employed get equation traveling wave exact equation. Our results reveal rational ur(x+νt) simply periodic us,1(x+νt) are solitary solutions, while us,2(x+νt) not real-valued. Finally, comput...

In this present study, the exact traveling wave solutions to the time fractional generalized Hirota-Satsuma coupled KdV system are studied by using the direct algebraic method. The exact and complex solutions obtained during the present investigation are new, whereas literature survey has revealed generalizations of solutions. The solutions obtained during the present work demonstrate the fact ...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...