Conte Truncated Expansion and Applications |
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| Authors: | Yufeng Zhang Qingyou Yan |
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| Institution: | (1) School of Information Science and Engineering, Shandong University of Science and Technology, Taian, People's Republic of China;(2) Academy of Mathematics and Systems Sciences, Academia Sinica, Institute of Computational Mathematics, Beijing, People's Republic of China;(3) Department of Economics and Statistics, Shandong Finance Institute, Jinan, People's Republic of China;(4) School of Mechanical Engineering, Dalian University of Technology, Dalian Liaoning, People's Republic of China |
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| Abstract: | In the special Conte truncated expansion approach one obtains different solutions of the Prigogine–Lefever equation by use of various solutions of a type of Riccati equation, including the periodic soliton solutions and singular soliton solutions. In order to acquire conveniently the soliton solutions of the Boussinesq equation, a proper transformation is applied. Using the special Conte truncated expansion approach yields the known bell-shape solutions and some new soliton solutions like cot2 × sec2, tan2 × c sec2, tanh2 × sech2, etc. We also study the soliton solutions of the modified Burgers equation (MBE). Using leading term analysis, we find the exponent is a fraction, i.e., –
. Therefore, the special Conte truncated expansion approach cannot be used directly. A transformation is first made to them another form of the MBE. Various soliton solutions of MBE are then presented, including the periodic solutions and singular soliton solutions. |
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| Keywords: | truncate expansion exact solution Riccati equation |
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