| 达布变换与(2+1)维Gardner方程的新解 |
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| 引用本文： | 扎其劳. 达布变换与(2+1)维Gardner方程的新解[J]. 内蒙古大学学报(自然科学版), 2010, 41(2) |
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| 作者姓名： | 扎其劳 |
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| 作者单位： | 内蒙古师范大学数学科学学院,呼和浩特,010022 |
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| 基金项目： | supported by the Natural Science Foundation of Inner Mongolia(Grant No.2009MS0108);;the Natural Science Foundation(Grant No ZRYB08017);;the Initial Fundingof Scientific Research Project for Ph.D of Inner Mongolia Normal University~~ |
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| 摘 要： | 近期,耿献国和曹策问将(2+1)维Gardner方程分解到两个(1+1)维孤子方程.本文计算出这两个(1+1)维孤子方程的Lax对,并利用Lax对的规范变换构造了该(1+1)维孤子方程的新达布变换.应用达布变换和分解获得了(2+1)维Gardner方程的一些新显式解,其中包括多孤子解.
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| 关 键 词： | 达布变换 孤子解 （2+1）维Gardner方程 |
Darboux Transformation and New Solutions for the (2+1)-dimensional Gardner Equation |
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| Zhaqilao. Darboux Transformation and New Solutions for the (2+1)-dimensional Gardner Equation[J]. Acta Scientiarum Naturalium Universitatis Neimongol, 2010, 41(2) |
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| Authors: | Zhaqilao |
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| Affiliation: | College of Mathematics Science/a>;Inner Mongolia Normal University/a>;Hohhot 010022/a>;China |
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| Abstract: | Recently,the(2+1)-dimensional Gardner equation was decomposed into two known(1+1)-dimensional soliton equations by Geng and Cao.In this paper,the Lax pairs of the two(1+1)-dimensional soliton equations are derived.A new Darboux transformation of the two known(1+1)-dimensional soliton equations is constructed with the help of a gauge transformation of the Lax pairs.As an application of the Darboux transformation and the decomposition,some new explicit solutions of the(2+1)-dimensional Gardner equation are ob... |
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| Keywords: | Darboux transformation soliton solution (2+1)-dimensional Gardner equation |
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