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Exact Solutions and Numerical Simulation of the Discrete Sawada–Kotera Equation

Department of Applied Mathematics, Yuri Gagarin State Technical University of Saratov, Politekhnicheskaya str. 77, Saratov 410054, Russia
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Symmetry 2020, 12(1), 131; https://doi.org/10.3390/sym12010131
Received: 17 December 2019 / Revised: 5 January 2020 / Accepted: 6 January 2020 / Published: 9 January 2020
(This article belongs to the Special Issue Asymptotic Methods in the Mechanics and Nonlinear Dynamics)
We investigated an integrable five-point differential-difference equation called the discrete Sawada–Kotera equation. On the basis of the geometric series method, a new exact soliton-like solution of the equation is obtained that propagates with positive or negative phase velocity. In terms of the Jacobi elliptic function, a class of new exact periodic solutions is constructed, in particular stationary ones. Using an exponential generating function for Catalan numbers, Cauchy’s problem with the initial condition in the form of a step is solved. As a result of numerical simulation, the elasticity of the interaction of exact localized solutions is established. View Full-Text
Keywords: discrete Sawada–Kotera equation; exact solution; Jacobi elliptic functions; Catalan numbers; numerical simulation discrete Sawada–Kotera equation; exact solution; Jacobi elliptic functions; Catalan numbers; numerical simulation
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Zemlyanukhin, A.; Bochkarev, A. Exact Solutions and Numerical Simulation of the Discrete Sawada–Kotera Equation. Symmetry 2020, 12, 131.

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