Soliton wave solutions of ion-acoustic waves a cold plasma with negative ions

Abstract

This article investigates the computational complex wave solutions of the modified Korteweg–de Vries equation combined with an adverse order of the Korteweg–de Vries model. This model was derived in 2017, where the recursion and inverse recursion operators are employed to select the integrable merged MKdV with a negative MKdV model. This integrable property is tested utilizing the Painlevé property. Verosky gave the description and properties of the opposing order recursion operator. We handle this model by implementing eleven contemporary techniques. We obtain a novel formula of complex solitary wave solutions for this model. Complex solitary wave solutions describe wave propagation, and it is also considered more mathematically concise tools to explain more details about the physical properties of models. The main goals of our paper are a comparison between these methods and introducing a novel modified method. All solutions are checked for accuracy by putting them back into the model via two different software (Maple 17 and Mathematica 12).