| 构造非线性发展方程无穷序列复合型精确解的一种方法 |
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| 引用本文： | 套格图桑. 构造非线性发展方程无穷序列复合型精确解的一种方法[J]. 物理学报, 2011, 60(1): 10202-010202 |
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| 作者姓名： | 套格图桑 |
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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： | 国家自然科学基金(批准号:10461006),内蒙古自治区高等学校科学研究基金(批准号:NJZZ07031),内蒙古自治区自然科学基金(批准号:2010MS0111)和内蒙古师范大学自然科学研究计划(批准号:QN005023)资助的课题. |
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| 摘 要： | 为了获得非线性发展方程新的无穷序列复合型精确解,给出了Riccati方程的Bäcklund变换和解的非线性叠加公式,符号计算系统Mathematica的帮助下,以广义Boussinesq方程为应用实例,获得了无穷序列复合型精确解.这里包括双曲函数、三角函数与有理函数复合解、双曲函数与三角函数复合解等几种新的无穷序列复合型精确解.该方法在构造非线性发展方程无穷序列复合型精确解方面具有普遍意义.关键词：非线性发展方程非线性叠加公式Riccati方程无穷序列精确解
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| 关 键 词： | 非线性发展方程 非线性叠加公式 Riccati方程 无穷序列精确解 |
| 收稿时间： | 2010-01-29 |
A method for constructing infinite sequence complexiton solutions to nonlinear evolution equations |
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| Taogetusang. A method for constructing infinite sequence complexiton solutions to nonlinear evolution equations[J]. Acta Physica Sinica, 2011, 60(1): 10202-010202 |
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| Authors: | Taogetusang |
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| Affiliation: | The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China |
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| Abstract: | To seek new infinite sequence complexiton solutions to nonlinear evolution equations(NEE(s)), the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation are presented, and as an illusrative exapmle, the generalized Boussinesq equation is chosen to obtain new infinite sequence complexiton solutions with the aid of symbolic computation system Mathematica, which includes complexiton solutions of hyperbolic function, triangular function type with rational function and hyperbolic function with triangular function. The method is of significance to construct infinite sequence complexiton solutions to other NEEs. |
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| Keywords: | nonlinear evolution equation formula of nonlinear superposition Riccati equation infinite sequence exact solution |
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