Abstract
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.
Funding source: UGC (India)
Award Identifier / Grant number: F1-17.1/201718/RGNF-2017-18-SC-ORI-39488
Funding source: Durban University of Technology
Funding source: National Research Foundation of South Africa
Funding source: University of KwaZulu-Natal
Acknowledgments
AKH expresses grateful thanks to UGC (India), NFSC, Award No. F1-17.1/201718/RGNF-2017-18-SC-ORI-39488 for financial support and Late Prof. K.M. Tamizhmani for the discussions which AKH had with him which formed the basis of this work. PGLL acknowledges the support of the National Research Foundation of South Africa, the University of KwaZulu-Natal and the Durban University of Technology.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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