| 一个可积非线性演化方程的达布变换及其精确解 |
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| 引用本文： | 马云苓,曾昕,耿献国. 一个可积非线性演化方程的达布变换及其精确解[J]. 郑州大学学报(自然科学版), 2012, 0(2): 31-34 |
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| 作者姓名： | 马云苓 曾昕 耿献国 |
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| 作者单位： | [1]商丘师范学院数学系,河南商丘476000 [2]郑州大学数学系,河南郑州450001 |
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| 基金项目： | 国家自然科学基金资助项目,编号11171312,11001250. |
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| 摘 要： | 研究了一个新的可积非线性演化方程,基于其Lax对和谱问题的规范变换,构造出该方程的一个达布变换,进而利用此达布变换,得到该方程的精确解,包括有理解、孤子解与周期解.
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| 关 键 词： | 非线性演化方程 达布变换 精确解 |
Darboux Transformation and Exact Solutions for an Integrable Nonlinear Evolution Equation |
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| MA Yun-ling,ZENG Xin,GENG Xian-guo. Darboux Transformation and Exact Solutions for an Integrable Nonlinear Evolution Equation[J]. Journal of Zhengzhou University (Natural Science), 2012, 0(2): 31-34 |
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| Authors: | MA Yun-ling ZENG Xin GENG Xian-guo |
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| Affiliation: | 1. Department of Mathematics, Shangqiu Normal University, Shangqiu 476000, China ; 2. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China) |
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| Abstract: | A new integrable nonlinear evolution equation was proposed. Based on the resulting Lax pair,a Darboux transformation of the nonlinear evolution equation was structured with the aid of the gauge transformation, by which some exact solutions of the nonlinear evolution equation were obtained, inclu- ding rational solutions, soliton solutions and periodic solutions. |
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| Keywords: | nonlinear evolution equation Darboux transformation exact solution |
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