New Periodic and Localized Traveling Wave Solutions to a Kawahara-Type Equation: Applications to Plasma Physics

In this study, some new hypotheses and techniques are presented to obtain some new analytical solutions (localized and periodic solutions) to the generalized Kawahara equation (gKE). As a particular case, some traveling wave solutions to both Kawahara equation (KE) and modified Kawahara equation (mKE) are derived in detail. Periodic and soliton solutions to this family are obtained. The periodic solutions are expressed in terms of Weierstrass elliptic functions (WSEFs) and Jacobian elliptic functions (JEFs). For KE, some direct and indirect approaches are carried out to derive the periodic and localized solutions. For mKE, two different hypotheses in the form of WSEFs are used to derive the periodic and localized solutions. Also, the cnoidal wave solutions in the form of JEFs are obtained. As a realistic physical application, the solutions obtained can be dedicated to studying many nonlinear waves that propagate in plasma.