| Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term简 |
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| 引用本文： | 李想,张卫国,李正明. Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term简[J]. 应用数学和力学(英文版), 2014, 35(1): 117-132. DOI: 10.1007/s10483-014-1777-7 |
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| 作者姓名： | 李想 张卫国 李正明 |
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| 基金项目： | Project supported by the National Naturai Science Foundation of China （No. 11071164）, the Inno vation Program of Shanghai Municipal Education Commission （No. 13ZZl18）, the Shanghai Leading Academic Discipline Project （No. XTKX2012）, and the Innovation Fund Project for Graduate Stu dent of Shanghai （No. JWCXSL1201） |
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| 摘 要： | This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
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| 关 键 词： | nonlinear wave equation bounded traveling wave solution shape analysis approximate damped oscillatory solution error estimate |
| 收稿时间： | 2013-05-20 |
Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term |
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| Xiang Li,Wei-guo Zhang,Zheng-ming Li. Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term[J]. Applied Mathematics and Mechanics(English Edition), 2014, 35(1): 117-132. DOI: 10.1007/s10483-014-1777-7 |
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| Authors: | Xiang Li Wei-guo Zhang Zheng-ming Li |
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| Affiliation: | 1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China |
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| Abstract: | This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and conditions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approximate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate solutions. It can be seen that the error is infinitesimal decreasing in the exponential form. |
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| Keywords: | nonlinear wave equation bounded traveling wave solution shape analysis approximate damped oscillatory solution error estimate |
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