Factorization method for some inhomogeneous Lienard equations

Abstract

We obtain closed-form solutions of several inhomogeneous Lienard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the forcing term. In this way, one can find the forcing terms that lead to integrable cases. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. The illustrative examples of Lienard solutions obtained in this way generically have rational parts, and consequently display singularities.

arXiv comment4 pages, 0 figures, published version

References in corpus (4)

• Supersymmetric pairing of kinks for polynomial nonlinearities
• Nonlinear second order ODE's: Factorizations and particular solutions
• New aspects of integrability of force-free Duffing-van der Pol oscillator and related nonlinear systems
• Extension of a factorization method of nonlinear second order ODE's with variable coefficients

Cited by in corpus (1)

• Factorization conditions for nonlinear second-order differential equations