On the complete integrability and linearization of nonlinear ordinary differential equations - Part IV: Coupled second order equations

Abstract

Coupled second order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations we focus our attention on the method of deriving general solution of two coupled second order nonlinear ordinary differential equations through the extended Prelle-Singer procedure. We describe a procedure to obtain integrating factors and required number of integrals of motion so that the general solution follows straightforwardly from these integrals. Our method tackles both isotropic and non-isotropic cases in a systematic way. In addition to the above, we introduce a new method of transforming coupled second order nonlinear ODEs into uncoupled ones. We illustrate the theory with potentially important examples.

minor revision in section 2 and added a new reference. Proc. R. Soc. London A (accepted)

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Cited by in corpus (5)

• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations
• Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second order differential equations
• Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation
• On the complete integrability and linearization of nonlinear ordinary differential equations - Part V: Linearization of coupled second order equations
• Exact solutions of coupled Liénard-type nonlinear systems using factorization technique