The Solutions of Nonlinear Heat Conduction Equation via Fibonacci&Lucas Approximation Method

2015/11/04 by Zehra Pinar, Pinar, Zehra, Turgut Ozis +1 · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #math-ph #math.AP #math.MP #nlin.PS #nlin.SI

paper · pdf · doi:10.48550/arxiv.1511.01787

15 pages

arxiv created 2015/11/04 · arxiv updated 2015/11/06

Abstract

To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas type equations. The proposed Fibonnacci&Lucas approximation method produces many new solutions. Consequently, we introduce new exact travelling wave solutions of some physical systems in terms of these new solutions of the Fibonacci&Lucas type equation. In addition to using different ansatz, we use determine different balancing principle to obtain optimal solutions.

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• A remark on a variable-coefficient Bernoulli equation based on auxiliary -equation method for nonlinear physical systems

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