Conserved Vectors, Analytic Solutions and Numerical Simulation of Soliton Collisions of the Modified Gardner Equation
Chaudry Masood Khalique,
Carel Olivier,
Boikanyo Pretty Sebogodi
Affiliations
Chaudry Masood Khalique
Material Science, Innovation and Modelling Research Focus Area, Department of Mathematics and Applied Mathematics, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
Carel Olivier
Pure and Applied Analytics, Department of Mathematics and Applied Mathematics, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
Boikanyo Pretty Sebogodi
Material Science, Innovation and Modelling Research Focus Area, Department of Mathematics and Applied Mathematics, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
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.
