Conte Truncated Expansion and Applications

Authors: Zhang Y.¹; Yan Q.²

Source: International Journal of Theoretical Physics, Volume 42, Number 12, December 2003 , pp. 3011-3018(8)

Publisher: Springer

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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., -½. 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.

Keywords: truncate expansion; exact solution; Riccati equation

Document Type: Research article

Affiliations: 1: School of Information Science and Engineering, Shandong University of Science and Technology, Taian, People's Republic of China. Institute of Computational Mathematics, Academy of Mathematics and Systems Sciences, Academia Sinica, Beijing, People's Republic of China; , yanqingyou@263.net, Email: zhang_yfshandong@163.com 2: Department of Economics and Statistics, Shandong Finance Institute, Jinan, People's Republic of China. School of Mechanical Engineering, Dalian University of Technology, Dalian Liaoning, People's Republic of China

Publication date: 2003-12-01