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Group analysis to the time fractional nonlinear wave equation
- Source :
- International Journal of Mathematics. 31:2050029
- Publication Year :
- 2020
- Publisher :
- World Scientific Pub Co Pte Lt, 2020.
-
Abstract
- In this paper, we mainly investigate the time fractional nonlinear wave equation which can be usually used to express nonlinear phenomena appearing in shallow water waves by using group analysis scheme. First, the symmetry can be obtained make uses of the group analysis to the time fractional nonlinear wave equation. Based on the above-found symmetry, this equation was able to reduce into an ordinary differential equation of fractional order. As a result, some new invariant solutions were also constructed for this considered equation. Second, the scaling transformation was also obtained by introducing new independent and dependent variables. Finally, the conservation laws were also found to satisfy the time fractional nonlinear wave equation with the help of the Ibragimov theorem. These novel results show unique nonlinear phenomena.
Details
- ISSN :
- 17936519 and 0129167X
- Volume :
- 31
- Database :
- OpenAIRE
- Journal :
- International Journal of Mathematics
- Accession number :
- edsair.doi...........abe9af5ac81d1e05413282d9730c79c6