一类广义鸭解系统的同伦映射解

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1502-1506.

一类广义鸭解系统的同伦映射解

莫嘉琪

安徽师范大学数学系安徽芜湖 241003|上海高校计算科学E-研究院SJTU研究所上海 200240

收稿日期:2010-05-08 修回日期:2011-09-06 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
国家自然科学基金$(40876010)、中国科学院知识创新工程重要方向项目(KZCX2-YW-Q03-08)、公益性行业科研专项(GYHY200806010)、
LASG国家重点实验室专项经费、上海市教育委员会E-研究院建设计划项目(E03004)、安徽高校省级自然科学研究重点项目(KJ2011A135)和浙江省自然科学基金(Y6110502)资助

Homotopic Mapping Solution for a Class of Generalized Canard Systems

MO Jia-Qi

Department of Mathemtics, Anhui Normal University, Anhui Wuhu 241003|Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 200240

Received:2010-05-08 Revised:2011-09-06 Online:2011-12-25 Published:2011-12-25
Supported by:
国家自然科学基金$(40876010)、中国科学院知识创新工程重要方向项目(KZCX2-YW-Q03-08)、公益性行业科研专项(GYHY200806010)、
LASG国家重点实验室专项经费、上海市教育委员会E-研究院建设计划项目(E03004)、安徽高校省级自然科学研究重点项目(KJ2011A135)和浙江省自然科学基金(Y6110502)资助

摘要/Abstract

摘要：

利用同伦映射理论研究了一类广义鸭解系统. 首先引入一组同伦映射. 然后构造了原系统解的迭代关系式. 最后得到了问题鸭解的近似解析式.

关键词: 鸭解, 孤子, 同伦映射

Abstract:

Using the homotopic mapping theory, the approximations of the solution for generalized canard systems are obtained. Firstly, introducing a set of homotopic mapping. Then the iteration expressions of solution for original system are constructed. Finally, the analytic expressions of the canard solution for problem are obtained.

Key words: Canard solution, Soliton, Homotopic mapping

中图分类号:

34E15

莫嘉琪. 一类广义鸭解系统的同伦映射解[J]. 数学物理学报, 2011, 31(6): 1502-1506.

MO Jia-Qi. Homotopic Mapping Solution for a Class of Generalized Canard Systems[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1502-1506.

参考文献

[1] Li Cuiping. Duck problem in the singular perturbation. Science in China (Ser A), 1999, 29(12): 1084--1093

[2] Xie F, Han M A, Zhang W J. The persistence of canards in 3-D singularly perturbed systems with two fast variables. Asymptotic Anal, 2006, 47(1): 95--106

[3] Ei S I, Mimura M, Nagayama M. Interacting spots in reaction diffusion systems. Discrete Contin Dyn Syst, 2006, 14(1): 31--62

[4] Xu Y, Zhang J X, Zu X, Zhou H. Nonchaotic random behaviour in the second order autonomous system. Chin Phys, 2007, 16(8): 2285--2290

[5] Wang M L. Solitary wave solutions for variant Boussinesq equations. Phys Lett A, 1995, 199(3/4): 169--172

[6] Sirendaoreji S J. Auxiliary equation method for solving nonlinear partial differential equations. Phys Lett A, 2003, 309(5/6): 387--396

[7] McPhaden M J, Zhang D. Slowdown of the meridional overturning circulation in the upper Pacific ocean. Nature, 2002, 415(3): 603--608

[8] Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Method. New York: CRC Press Co, 2004

[9] He J H. Approximate Analytical Methods in Engineering and Sciences (in Chinese). Zhengzhou: Henan Science and Technology Press, 2002

[10] Mo J Q. A class of singulaely perturbed differential-difference reaction diffusion equations. Adv Math, 2009, 38(2): 227--230

[11] Mo J Q, Lin W T. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations. J Sys Sci & Complexity, 2008, 20(1): 119--128

[12] Mo J Q. Approximate solution of homotopic mapping to solitary for generalized nonlinear KdV system. Chin Phys Lett, 2009, 26(1): 010204-1--010204-4

[13] Mo J Q. A variational iteration solving method for a class of generalized Boussinesq equations. Chin Phys Lett, 2009, 26(6): 060202-1--060202-3

[14] Mo J Q. A class of homotopic solving method for ENSO mpdel. Acta Math Sinica, 2009, 29(1): 101--109

[15] Mo J Q, Zhang W J, He M. Asymptotic method of traveling wave solutions for a class of nonlinear reaction diffusion equation. Acta Math Sinica, 2007, 27B(4): 777--780

[16] 莫嘉琪, 唐荣荣. 反应扩散方程解的渐近性态.数学物理学报, 2007, 27A(2): 296--301

[17] 莫嘉琪. 一类拟线性Robin问题的激波解. 数学物理学报, 2008, 28A(5): 818--822

[18] Mo Jiaqi, Wang Hui, Lin Wantao. The solvability for a class of singularly perturbed quasi-linear differential system. Acta Math Sci, 2008, 28B(3): 495--500

[19] Mo Jiaqi, Lin Wantao, Wang Hui. A class of homotopic solving method for ENSO model. Acta Math Sci, 2009, 29B(1): 101--110