| Abstract: |
| This article investigates the first integrals and closed form solutions of some non-linear first order
dynamical systems from diverse areas of applied mathematics. We introduce the notion of artificial
Hamiltonian and we show that every first order system of ordinary differential equations (ODEs) can be written in the form of an artificial Hamiltonian system. One can also express the second order ODE or
system of second order ODEs in the form of system of first order artificial Hamiltonian system. Then the partial Hamiltonian approach is employed to compute the partial Hamiltonian operators and the
corresponding first integrals. The first integrals are utilized to construct the closed form solutions of
laser photon model, duffing van-der pol oscillator and nonlinear optical oscillators under parameter
restrictions. We show that how one can apply the existing partial Hamiltonian approach for nonstandard Hamiltonian systems. This study provides a new way of solving the dynamical systems of first
order ODEs, second order ODE and second order systems of ODEs which are expressed into the artificial Hamiltonian system. |
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