Analytic solution to the generalized complex Duffing equation and its application in soliton theory

ABSTRACT

In this paper, we give the analytical solution to the generalized Duffing equation with complex coefficients subjected to an arbitrary given initial conditions. We provide the solution in terms of the famous Weierstrass elliptic function. This solution is used to obtain the flow of the dynamical system associated to Duffing equation. We illustrate the obtained results by means of applications in Soliton Theory.

Keywords:

• Jacobi elliptic function
• elliptic modulus
• Duffing oscillator
• cubic nonlinearity
• exact solutions
• approximate solutions
• free vibrations
• forced vibrations
• Parametric vibrations
• chaos

2010 Mathematics Subject Classification:

• 34Axx

Disclosure statement

No potential conflict of interest was reported by the author.