Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation

• Published in: arXiv.org
• Main Authors: Ghosh, Uttam, Sarkar, Susmita, Das, Shantanu
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 25.02.2016
• Subjects: Applications of mathematics; Burgers equation; Computer simulation; Exact solutions; Mathematical models; Mathematics - Analysis of PDEs; Nonlinear analysis; Nonlinear differential equations; Nonlinear equations; Partial differential equations; Physics - Exactly Solvable and Integrable Systems; Physics - Pattern Formation and Solitons
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1602.09083

Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The exact solution obtained by fractional sub-equation method reduces to classical solution when order of fractional derivative tends to one. Finally numerical simulation has done. The numerical simulation justifies that the solutions of two fractional differential equations reduces to shock solution for KP-Burger equation and soliton solution for coupled KdV equations when order of derivative tends to one.