Conserved Vectors, Analytic Solutions and Numerical Simulation of Soliton Collisions of the Modified Gardner Equation

Abstract

This paper aims to study the modified Gardner (mG) equation that was proposed in the literature a short while ago. We first construct conserved vectors of the mG equation by invoking three different techniques; namely the method of multiplier, Noether's theorem, and the conservation theorem owing to Ibragimov. Thereafter, we present exact solutions to the mG equation by invoking a complete discrimination system for the fifth degree polynomial. Finally, we simulate collisions of solitons for the mG equation.