New super and shock like solitary structures for KdV equation with higher-order nonlinearity

Abstract

The model of dual-power law nonlinearity Korteweg–De Vries (KdV) equation describe sudden physical phenomena with higher orders of nonlinearity in fluid dynamics, plasma, fiber communications and biological systems. The model was solved by the modified F-expansion approach to produce structural solutions in the vital form of super periodic solitons, super periodic shocks, shock solutions, super-shock-soliton like solutions and cnoidal solitons. The modified F-expansion approach is an effective, powerful and straightforward method for obtaining the solitary wave solutions to the nonlinear partial differential equations (NPDEs). The effect of model parameters on the nature, properties and structures of the model solutions have been examined. It was noted that, the wave amplitude, bandwidths and phase shift are improved by changing model parameters in super periodic solitons and super periodic shocks. The new solutions obtained in this study may hold significance for the applications of electrostatic EASWs structures at critical density, which have been observed in diverse space plasma environments, including the plasma sheet boundary layers of the Earth’s magnetotail region for ions temperature ranging from 0.01 to 1 KeV.