Journal
INTERNATIONAL JOURNAL OF MATHEMATICS
Volume 31, Issue 4, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129167X20500299
Keywords
Group analysis; time fractional nonlinear wave equation; scaling transformation; invariant solutions; conservation laws
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Funding
- China University of Mining and Technology [102504180004]
- 333 Project of Jiangsu Province [BRA2018320]
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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.
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