Volume 12, Issue 1
Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena

Mohamed R. Ali, Wen-Xiu Ma & R. Sadat

East Asian J. Appl. Math., 12 (2022), pp. 201-212.

Published online: 2021-10

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  • Abstract

We present Lie symmetry analysis to explore solitary wave solutions, two-soliton type solutions and three-soliton type solutions in variable-coefficient nonlinear physical phenomena. An example is a (2+1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko (VCBK) equation. We compute the Lie algebra of infinitesimals of its symmetry vector fields and an optimal system of one-dimensional sub-Lie algebras of the resulting symmetries. Two stages of Lie symmetry reductions will be built to reduce the VCBK equation to nonlinear ordinary differential equations (ODEs) and new analytical solutions to those ODEs will be found by using the integration method. Some of such resulting solutions to the VCBK equation and their dynamics will be illustrated through three-dimensional plots.

  • Keywords

Symmetry analysis, partial differential equations, the variable coefficients (2+1)-dimensional Bogoyavlensky-Konopelchenko equation.

  • AMS Subject Headings

76M60, 35Q51, 35C99, 68W30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-201, author = {Ali , Mohamed R. and Ma , Wen-Xiu and Sadat , R.}, title = {Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {12}, number = {1}, pages = {201--212}, abstract = {

We present Lie symmetry analysis to explore solitary wave solutions, two-soliton type solutions and three-soliton type solutions in variable-coefficient nonlinear physical phenomena. An example is a (2+1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko (VCBK) equation. We compute the Lie algebra of infinitesimals of its symmetry vector fields and an optimal system of one-dimensional sub-Lie algebras of the resulting symmetries. Two stages of Lie symmetry reductions will be built to reduce the VCBK equation to nonlinear ordinary differential equations (ODEs) and new analytical solutions to those ODEs will be found by using the integration method. Some of such resulting solutions to the VCBK equation and their dynamics will be illustrated through three-dimensional plots.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.100920.060121}, url = {http://global-sci.org/intro/article_detail/eajam/19928.html} }
TY - JOUR T1 - Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena AU - Ali , Mohamed R. AU - Ma , Wen-Xiu AU - Sadat , R. JO - East Asian Journal on Applied Mathematics VL - 1 SP - 201 EP - 212 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.100920.060121 UR - https://global-sci.org/intro/article_detail/eajam/19928.html KW - Symmetry analysis, partial differential equations, the variable coefficients (2+1)-dimensional Bogoyavlensky-Konopelchenko equation. AB -

We present Lie symmetry analysis to explore solitary wave solutions, two-soliton type solutions and three-soliton type solutions in variable-coefficient nonlinear physical phenomena. An example is a (2+1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko (VCBK) equation. We compute the Lie algebra of infinitesimals of its symmetry vector fields and an optimal system of one-dimensional sub-Lie algebras of the resulting symmetries. Two stages of Lie symmetry reductions will be built to reduce the VCBK equation to nonlinear ordinary differential equations (ODEs) and new analytical solutions to those ODEs will be found by using the integration method. Some of such resulting solutions to the VCBK equation and their dynamics will be illustrated through three-dimensional plots.

Mohamed R. Ali, Wen-Xiu Ma & R. Sadat. (2021). Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena. East Asian Journal on Applied Mathematics. 12 (1). 201-212. doi:10.4208/eajam.100920.060121
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