| 非线性弦振动方程的孤子解、周期孤立波解和拟周期解 |
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| 引用本文： | 王媛,徐桂琼. 非线性弦振动方程的孤子解、周期孤立波解和拟周期解[J]. 西北师范大学学报(自然科学版), 2010, 0(6) |
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| 作者姓名： | 王媛 徐桂琼 |
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| 作者单位： | 上海大学理学院;上海大学管理学院; |
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| 基金项目： | 国家自然科学基金资助项目(10801037) |
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| 摘 要： | 利用Hirota双线性方法,首先得到了非线性弦振动方程的孤子解,图形分析表明,此方程存在阶梯状的双向孤子解,既包括迎面型碰撞的孤子解,也包括追赶型碰撞的孤子解.其次,得到了非线性弦振动方程4种类型的周期孤立波解.最后,借助于Riemann theta函数,得到了非线性弦振动方程的拟周期解,在极限情况下,该拟周期解可以退化为孤子解.
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| 关 键 词： | 非线性弦振动方程 Hirota双线性方法 孤子解 周期孤立波解 拟周期解 |
Soliton solutions,periodic solitary and quasi-periodic wave solutions for a nonlinear vibrating string equation |
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| WANG Yuan,XU Gui-qiong. Soliton solutions,periodic solitary and quasi-periodic wave solutions for a nonlinear vibrating string equation[J]. Journal of Northwest Normal University Natural Science (Bimonthly), 2010, 0(6) |
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| Authors: | WANG Yuan XU Gui-qiong |
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| Affiliation: | WANG Yuan1,XU Gui-qiong2 (1.College of Sciences,Shanghai University,Shanghai 200444,China,2.College of Management,China) |
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| Abstract: | By using of the Hirota bilinear method,the soliton solutions of the nonlinear vibrating string equation are obtained.The nonlinear vibrating string equation admits up-stair shape bidirectional soliton solutions,which represent the head-on collisions between solitary waves as well as overtaking ones.Then,four types of periodic solitary wave solutions are derived for the nonlinear vibrating string equation.Moreover,the quasi-periodic wave solutions are also given for the nonlinear vibrating string equation by... |
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| Keywords: | nonlinear vibrating string equation Hirota bilinear method soliton solution periodic solitary wave solution quasi-periodic wave solution |
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