A qualitative study of the damped duffing equation and applications

abstract

• In this paper, we analyze the damped Duffing equation by means of qualitative theory of planar systems. Under certain parametric choices, the global structure in the Poincar phase plane of an equivalent two-dimensional autonomous system is plotted. Exact solutions are obtained by using the Lie symmetry and the coordinate transformation method, respectively. Applications of the second approach to some nonlinear evolution equations such as the two-dimensional dissipative Klein-Gordon equation are illustrated.

authors

• Chen, Goong

published proceedings

• DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

author list (cited authors)

• Feng, Z., Chen, G., & Hsu, S.

citation count

• 21

complete list of authors

• Feng, Zhaosheng||Chen, Goong||Hsu, Sze-Bi

publication date

• September 2006

publisher

• American Institute of Mathematical Sciences (AIMS)  Publisher

published in

• Discrete and Continuous Dynamical Systems Series B: a journal bridging mathematics and sciences  Journal

keywords

• Autonomous System
• Duffing's Equation
• Equilibrium Point
• Global Structure
• Lie Symmetry
• Phase Plane

Digital Object Identifier (DOI)

• 10.3934/dcdsb.2006.6.1097

start page

• 1097

end page

• 1112

volume

• 6

issue

• 5

URL

• http://dx.doi.org/10.3934/dcdsb.2006.6.1097