In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact sol...In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.展开更多
This paper is concerned with the generalized variable-coefficient nonlinear evolution equation（vc-NLEE）.The complete integrability classification is presented,and the integrable conditions for the generalized variab...This paper is concerned with the generalized variable-coefficient nonlinear evolution equation（vc-NLEE）.The complete integrability classification is presented,and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlevé analysis.Then,the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method,and the Lax pairs（LP） of the vc-NLEEs are constructed in terms of the integrable conditions.展开更多
基金financially supported by the Key Research and Development Program of China(No.2022YFB2404102)the National Natural Science Foundation of China(Nos.51971093,52171158)the Key Research and Development Program of Shandong Province,China(Nos.2021ZLGX01,2022CXGC020308)。
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 11505090the Natural Science Foundation of Shandong Province under Grant No.ZR2015AL008the High-Level Personnel Foundation of Liaocheng University under Grant No.31805
文摘In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171041)the High-Level Personnel Foundation of Liaocheng University(Grant No.31805)
文摘This paper is concerned with the generalized variable-coefficient nonlinear evolution equation（vc-NLEE）.The complete integrability classification is presented,and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlevé analysis.Then,the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method,and the Lax pairs（LP） of the vc-NLEEs are constructed in terms of the integrable conditions.
