Abstract
A modification of the geometric series method is considered, which is suitable for obtaining exact solutions of nonlinear differential-difference equations. The features of the method are shown in examples of solving three-point and five-point equations, the right-hand sides of which can contain polynomials, rational fractions, explicitly given elementary functions and implicitly defined functions that are solutions of some differential equations. The advantages and disadvantages of the approach are noted in comparison with other methods for constructing exact solutions.
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The reported study was funded by RFBR, project number 20-01-00123.
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Zemlyanukhin, A.I., Bochkarev, A.V., Orlova, A.A., Ratushny, A.V. (2021). Geometric Series Method and Exact Solutions of Differential-Difference Equations. In: Abramian, A.K., Andrianov, I.V., Gaiko, V.A. (eds) Nonlinear Dynamics of Discrete and Continuous Systems. Advanced Structured Materials, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-53006-8_15
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DOI: https://doi.org/10.1007/978-3-030-53006-8_15
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