Generalized Jacobi Elliptic Solutions for the KdV Equation with Dual Power Law Non-Linearity and for the Power Law KdV-Burger Equation with the Source

• Published in: International journal of applied and computational mathematics Vol. 8; no. 3
• Main Authors: Dafounansou, Ousmanou, Ungem, Linus Bache, Mbah, David Christian, Nguenang, Jean Pierre
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied mathematics; Burgers equation; Computational mathematics; Computational Science and Engineering; Korteweg-Devries equation; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nonlinearity; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Power law; Theoretical; Jacobi elliptic; KdV and KdV-Burger equation; Power law; Expansion
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-022-01291-8

Within the framework of an improved Jacobi elliptic expansion method, we study the Jacobi elliptic solutions for the Korteweg-de Vries (KdV) equation with dual power law nonlinearity and the power law KdV-Burger equation with the source. We thus have for each equation, the opportunity to consider three cases: the lower order powers ( n = 1 , 2 ) and the higher order powers ( n ≥ 3 ). It turns out that a huge family of Jacobi elliptic solutions, subject to some conditions are obtained as solutions in the lower order powers cases, while the higher order powers that require strong constraints give us the elliptic solutions in the limits of the modulus.