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Halder, Amlan K.; Paliathanasis, Andronikos; Seshadri, Rajeswari; Leach, Peter G. L.

Lie symmetry analysis and similarity solutions for the Jimbo-Miwa equation and generalisations. (English) Zbl 07446870

Int. J. Nonlinear Sci. Numer. Simul. 21, No. 7-8, 767-779 (2020).
Summary: We study the Jimbo-Miwa equation and two of its extended forms, as proposed by Wazwaz et al., using Lie’s group approach. Interestingly, the travelling-wave solutions for all the three equations are similar. Moreover, we obtain certain new reductions which are completely different for each of the three equations. For example, for one of the extended forms of the Jimbo-Miwa equation, the subsequent reductions leads to a second-order equation with Hypergeometric solutions. In certain reductions, we obtain simpler first-order and linearisable second-order equations, which helps us to construct the analytic solution as a closed-form function. The variation in the nonzero Lie brackets for each of the different forms of the Jimbo-Miwa also presents a different perspective. Finally, singularity analysis is applied in order to determine the integrability of the reduced equations and of the different forms of the Jimbo-Miwa equation.

Cited in 2 Documents

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C14 Symmetries, invariants of ordinary differential equations
22E60 Lie algebras of Lie groups
35B06 Symmetries, invariants, etc. in context of PDEs
35C05 Solutions to PDEs in closed form
35C07 Traveling wave solutions

Keywords:

closed-form solution; similarity solutions; singularity analysis; symmetry analysis
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Full Text: DOI arXiv

References:

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