Solution and transcritical bifurcation of Burgers equation

doi:10.1088/1674-1056/20/2/020504

中国物理B ›› 2011, Vol. 20 ›› Issue (2): 20504-020504.doi: 10.1088/1674-1056/20/2/020504

Solution and transcritical bifurcation of Burgers equation

赵明华¹, 唐驾时², 韩峰², 张良²

(1)College of Civil Engineering, Hunan University, Changsha 410082, China; (2)College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China

收稿日期:2010-09-15 修回日期:2010-10-11 出版日期:2011-02-15 发布日期:2011-02-15

Solution and transcritical bifurcation of Burgers equation

Tang Jia-Shi(唐驾时)^a)^†,Zhao Ming-Hua(赵明华)^b), Han Feng(韩峰)^a),and Zhang Liang(张良)^a)

^a College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China; ^b College of Civil Engineering, Hunan University, Changsha 410082, China

Received:2010-09-15 Revised:2010-10-11 Online:2011-02-15 Published:2011-02-15

摘要/Abstract

摘要： Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics. We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region. The transcritical bifurcation exists in the (2+1)-dimensional Burgers equation.

关键词: Burgers equation, transcritical bifurcation, exact solution, bifurcation control

Abstract: Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics. We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region. The transcritical bifurcation exists in the (2+1)-dimensional Burgers equation.

Key words: Burgers equation, transcritical bifurcation, exact solution, bifurcation control

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

唐驾时, 赵明华, 韩峰, 张良. Solution and transcritical bifurcation of Burgers equation[J]. 中国物理B, 2011, 20(2): 20504-020504.

Tang Jia-Shi(唐驾时), Zhao Ming-Hua(赵明华), Han Feng(韩峰), and Zhang Liang(张良) . Solution and transcritical bifurcation of Burgers equation[J]. Chin. Phys. B, 2011, 20(2): 20504-020504.

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Solution and transcritical bifurcation of Burgers equation

Solution and transcritical bifurcation of Burgers equation

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