• A dynamical study of certain nonlinear diffusion–reaction equations with a nonlinear convective flux term

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/092/01/0008

• # Keywords

Nonlinear diffusion–reaction equation; Jacobi elliptic functions; kink–antikink soliton

• # Abstract

We explore the dynamics of quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux term, which arise in well-known physical and biological problems such as population dynamicsof the species. Three integration techniques, namely the $(G'/G)$-expansion method, its generalised version and Kudryashov method, are adopted to solve these equations. We attain new travelling and solitary wave solutions inthe form of Jacobi elliptic functions, hyperbolic functions, trigonometric functions and rational solutions with some constraint relations that naturally appear from the structure of these solutions. The travelling population fronts,which are the general solutions of nonlinear diffusion–reaction equations, describe the species invasion if higher population density corresponds to the species invasion. This effort highlights the significant features of the employed algebraic approaches and shows the diversity in the constructed solutions.

• # Author Affiliations

1. Department of Physics, Chaudhary Bansi Lal University, Bhiwani 127 021, India
2. Department of Physics, Pt. Neki Ram Sharma Government College, Rohtak 124 001, India
3. Department of Physics, Kurukshetra University, Kurukshetra 136 119, India

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019