| (2+1)维非线性演化方程的形式新解 |
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| 引用本文： | 马正义,朱加民. (2+1)维非线性演化方程的形式新解[J]. 中国计量学院学报, 2004, 15(2): 126-130,133 |
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| 作者姓名： | 马正义 朱加民 |
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| 作者单位： | 丽水学院,数学系,浙江,丽水,323000 |
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| 基金项目： | 浙江省自然科学基金资助项目(No.k203009) |
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| 摘 要： | 主要从两个方面讨论(1)将非线性演化方程的形式级数解进行对称延拓;(2)利用"秩"的概念,对非线性演化方程进行分类.即如果方程各项中"秩"的取值全为奇数或偶数,则可借助椭圆方程的方法解之;若方程各项中"秩"的取值奇偶性不一致,则给出一形式幂级数解.并以两个(2+1)维非线性演化方程为例,说明改进的方法能较好地求得非线性演化方程的更多形式新解.
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| 关 键 词： | 非线性演化方程 对称延拓 秩 形式解 |
| 文章编号： | 1004-1540(2004)02-0126-05 |
New format solutions for (2 + 1)-dimensional nonlinear evolution equations |
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| MA Zheng-yi,ZHU Jia-min. New format solutions for (2 + 1)-dimensional nonlinear evolution equations[J]. Journal of China Jiliang University, 2004, 15(2): 126-130,133 |
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| Authors: | MA Zheng-yi ZHU Jia-min |
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| Abstract: | The main ideas of this paper includes: (1) the ansatz solution of a nonlinear evolution equation is symmetrical extended; (2) nonlinear evolution equations are classified through the concept of "rank". In other words, we can solve them with the aid of the elliptic equation when "rank"values of every term in equations are odd or even. As examples, two (2 1)-dimensional nonlinear evolution equations are taken to show that the modified approach can obtain more new format solutions than before. |
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| Keywords: | nonlinear evolution equation symmetrical extension rank format solution |
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