Several soliton, solitary waves and their interactions for variable time dependent coefficient Burger’s equation

Abstract

We implement the explicit soliton solutions of the Burger's model of time dependent coefficient. Created by similarity transformation besides the generalized tanh function technique, we report several kinds of analytical solutions of the desired model. The essential and important feature of this study is the formulation of different sequences of explicit solutions of the Burger’s equation generated by the known solution of the model using the Backland transformations. Particularly, we investigate the emergent soliton and solitary constructions by a distinctive choice of the self-similar variable. Our consequences display the forms of both solitons and solitary waves can be usefully controlled by the detailed formula of the self-similar variable. The interaction of two and three soliton are discussed. We discuss how to construct another solution to some famous mathematical physical models such as KdVBurger’s, linear heat, coupled Burger’s and symmetric coupled Burger’s models from the known solution of Burger’s model.