Investigation of new solutions for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif equation

Mohamed R. ALI, R. SADAT, Wen-Xiu MA

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PDF(3414 KB)
Front. Math. China ›› 2021, Vol. 16 ›› Issue (4) : 925-936. DOI: 10.1007/s11464-021-0952-3
RESEARCH ARTICLE
RESEARCH ARTICLE

Investigation of new solutions for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif equation

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Abstract

We investigate and concentrate on new infinitesimal generators of Lie symmetries for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif (eCBS) equation using the commutator table which results in a system of nonlinear ordinary differential equations (ODEs) which can be manually solved. Through two stages of Lie symmetry reductions, the eCBS equation is reduced to non-solvable nonlinear ODEs using different combinations of optimal Lie vectors. Using the integration method and the Riccati and Bernoulli equation methods, we investigate new analytical solutions to those ODEs. Back substituting to the original variables generates new solutions to the eCBS equation. These results are simulated through three- and two-dimensional plots.

Keywords

Extended Calogero-Bogoyavlenskii-Schif (eCBS) equation / Riccati-Bernoulli equation / symmetry analysis / integrating factor / nonlinear integrable equations

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Mohamed R. ALI, R. SADAT, Wen-Xiu MA. Investigation of new solutions for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif equation. Front. Math. China, 2021, 16(4): 925‒936 https://doi.org/10.1007/s11464-021-0952-3

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