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| 1 | Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation显示文摘In this paper,we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation,namely Burgers-Kadomtsev-Petviashvili equation(Burgers-K-P)that arises in shallow water waves.Furthermore,using the residual power series method(RPSM),approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package.We also presented a few graphical illustrations for some surfaces.The fractional derivatives were considered in the conformable sense.All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method.The numerical outcomes confirmed that both methods are simple,robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations. | Mehmet Senol | 2020 | Communications in Theoretical Physics2020，72，5： | 0 |
| 2 | Bilinear forms through the binary Bell polynomials, N solitons and Backlund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach显示文摘Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-B?cklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and B?cklund transformations are different from those in the existing literature. All of our results are dependent on the waterwave dispersive power. | Xin-Yi Gao Yong-Jiang Guo Wen-Rui Shan | 2020 | Communications in Theoretical Physics2020，72，9： | 0 |
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