TAILIEUCHUNG - Lie symmetry analysis and exact solutions of the Sawada-Kotera equation

In the present paper, the Sawada–Kotera equation is considered by Lie symmetry analysis. All of the geometric vector fields to the Sawada–Kotera equation are obtained, and then the symmetry reductions and exact solutions of the Sawada–Kotera equation are investigated. Our results show that symmetry analysis is a very efficient and powerful technique in finding the solution of the proposed equation. | Turk J Math (2017) 41: 158 – 167 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Lie symmetry analysis and exact solutions of the Sawada–Kotera equation Youwei ZHANG∗ School of Mathematics and Statistics, Hexi University, Zhangye, . China Received: • Accepted/Published Online: • Final Version: Abstract: In the present paper, the Sawada–Kotera equation is considered by Lie symmetry analysis. All of the geometric vector fields to the Sawada–Kotera equation are obtained, and then the symmetry reductions and exact solutions of the Sawada–Kotera equation are investigated. Our results show that symmetry analysis is a very efficient and powerful technique in finding the solution of the proposed equation. Key words: Sawada–Kotera equation, Lie symmetry analysis, power series solution, hyperbolic function method, trial equation method, exact solution 1. Introduction Recently, the mathematics and physics fields have devoted considerable effort to the study of solutions to ordinary and partial differential equations (ODEs and PDEs). Among many powerful methods for solving equations, Lie symmetry analysis provides an effective procedure for integrability and conservation laws, reducing equations and exact solutions of a wide and general class of differential systems representing real physical problems [14, 18]. Sinkala et al. [17] performed the group classification of a bond-pricing PDE of mathematical finance to discover the combinations of arbitrary parameters that allow the PDE to admit a nontrivial symmetry Lie algebra, and they computed the admitted Lie point symmetries, identified the corresponding symmetry Lie algebra, and solved the PDE. Under the condition that the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution for PDEs, and a fundamental solution can be reduced to inverting a Laplace .

• Toán học
• Sawada Kotera equation
• Lie symmetry analysis
• Power series solution
• Hyperbolic function method
• Trial equation method
• Exact solution
• Vietnam Journal of Mechanics
• Non linear differential equations with exact solutions
• Finding the general exact solution
• Non linear equations
• General exact solution
• 4D noncommutative quantum field theory
• Non perturbative solution
• Integral equation
• Schwinger 2 point function
• Related matrix model
• BMC Bioinformatics
• Boolean modeling
• Exact method
• Stochastic model
• Asynchronous updating
• Steady state solution
• Continuous time Markov chain
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• Quasi exact solution
• Analytically solvable
• Levi Civita transformation
• Anharmonic oscillator potentials
• Harmonic oscillator
• Functionally graded material
• Classical plate theory
• Harmonic forced vibration
• Circular functionally graded plate
• Thickness of piezoelectric layer
• Non Fourier Conduction
• Harmonic Boundary Conditions
• Hyperbolic asymmetric heat
• Thermal displacement equation
• Long hollow cylinder
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• Corresponding basic functions
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