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Open AccessArticle

Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation

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Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
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Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan
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Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
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Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Al-Kharj 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 170; https://doi.org/10.3390/sym12010170
Received: 4 December 2019 / Revised: 28 December 2019 / Accepted: 8 January 2020 / Published: 16 January 2020
In this paper, we investigate a spatially two-dimensional Burgers–Huxley equation that depicts the interaction between convection effects, diffusion transport, reaction gadget, nerve proliferation in neurophysics, as well as motion in liquid crystals. We have used the Lie symmetry method to study the vector fields, optimal systems of first order, symmetry reductions, and exact solutions. Furthermore, using the power series method, a set of series solutions are obtained. Finally, conservation laws are derived using optimal systems. View Full-Text
Keywords: Burgers–Huxley equation; Lie symmetry method; conservation laws; Exact solutions Burgers–Huxley equation; Lie symmetry method; conservation laws; Exact solutions
MDPI and ACS Style

Hussain, A.; Bano, S.; Khan, I.; Baleanu, D.; Sooppy Nisar, K. Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation. Symmetry 2020, 12, 170.

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