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| Exact Periodic Solutions to Generalized BBM Equation and Relevant Conclusions | |
| 引用本文： | Jun-ying An Wei-guo Zhang. Exact Periodic Solutions to Generalized BBM Equation and Relevant Conclusions[J]. 应用数学学报(英文版), 2006, 22(3): 509-516. DOI: 10.1007/s10255-006-0326-3 |
| 作者姓名： | Jun-ying An Wei-guo Zhang |
| 作者单位： | University of Shanghai for Science and Technology, Shanghai 200093, China |
| 基金项目： | Supported by the National Science Foundation of Shanghai （No.03ZR14070） and Shanghai Leading Academic Discipline Project （No.T0502）. |
| 摘 要： | In this paper, we consider generalized BBM equation with nonlinear terms of high order.In the case of p=1/2, p=1 and p=2, the exact periodic solutions to G-BBM equation are obtained by means of proper transformation, which degrades the order of nonlinear terms. And we prove that if p ≠ 1/2,p ≠ 1 or p ≠ 2, G-BBM equation does not exist this kind of periodic solution. |
| 关 键 词： | Jacobi椭圆函数 非线性演化方程 周期解 广义BBM方程 |
| 收稿时间： | 2005-08-03 |
| 修稿时间： | 2005-08-03 |
Exact Periodic Solutions to Generalized BBM Equation and Relevant Conclusions |
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| Jun-ying An,Wei-guo Zhang. Exact Periodic Solutions to Generalized BBM Equation and Relevant Conclusions[J]. Acta Mathematicae Applicatae Sinica, 2006, 22(3): 509-516. DOI: 10.1007/s10255-006-0326-3 | |
| Authors: | Jun-ying An Wei-guo Zhang |
| Affiliation: | (1) University of Shanghai for Science and Technology, Shanghai, 200093, China |
| Abstract: | Abstract In this paper, we consider generalized BBM equation with nonlinear terms of high order. In the case of p=1/2, p=1 and p=2, the exact periodic solutions to G-BBM equation are obtained by means of proper transformation, which degrades the order of nonlinear terms. And we prove that if p ≠ 1/2, p ≠ 1 or p ≠ 2, G-BBM equation does not exist this kind of periodic solution. Supported by the National Science Foundation of Shanghai (No.03ZR14070) and Shanghai Leading Academic Discipline Project (No.TO502). |
| Keywords: | Jacobi elliptic function nonlinear evolution equation periodic solutions |
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