Factorization technique and isochronous condition for coupled quadratic and mixed Liénard-type nonlinear systems

• Presented a procedure to factorize coupled quadratic Liénard equation.
• Derived the isochronous condition and discussed the isochronous properties.
• Illustrated the procedure for a specific examples of physical interest.
• Discussed the factorization of coupled mixed Liénard type equation.

In this paper, we discuss a systematic and self consistent procedure to factorize a rather general class of coupled nonlinear ordinary differential equations (ODEs), namely coupled quadratic and mixed Liénard type equations, which include various physical and mathematical models. The procedure is broadly divided into two parts. In the first part, we consider a general factorized form for the equation under consideration in terms of some unknown functions and identify the determining equations for them. In the second part, we systematically solve the determining equations and identify the compatible factorizing form for this class of equations. In addition, we also discuss the problem of identification of isochronous dynamical systems belonging to the above class of equations. In particular, we deduce an isochronicity condition for the coupled quadratic Liénard equation. We also present specific examples of physical interest.