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A qualitative study of the damped Duffing equation and applications. (English) Zbl 1122.34001
The paper analyses the damped Duffing equation $$ x''+\delta x'-\mu x+x^3=0. \eqno{(1)} $$ In the first part of the paper the global structure of the phase plane is investigated using a detailed study of the vector field near infinity. The second part is devoted to the determination of exact solutions of (1) in terms of Jacobian elliptic functions by means of coordinate transformations. Application is given to travelling waves of the Klein-Gordon equation.

34A05Methods of solution of ODE
34C05Location of integral curves, singular points, limit cycles (ODE)
34C20Transformation and reduction of ODE and systems, normal forms
34C14Symmetries, invariants (ODE)
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