42 research outputs found
Non-existence criteria for Laurent polynomial first integrals
In this paper we derived some simple criteria for non-existence and partial non-existence Laurent polynomial first integrals for a general nonlinear systems of ordinary differential equations , with . We show that if the eigenvalues of the Jacobi matrix of the vector field are -independent, then the system has no nontrivial Laurent polynomial integrals
Random invariant manifolds and foliations for slow-fast PDEs with strong multiplicative noise
This article is devoted to the dynamical behaviors of a class of slow-fast PDEs perturbed by strong multiplicative noise. We will accomplish the existence of random invariant manifolds and foliations, and show exponential tracking property of them. Moreover, the asymptotic approximation for both objects will be presented
First integrals of the Maxwell–Bloch system
We investigate the analytic, rational and first integrals of the Maxwell–Bloch system
\begin{equation*}
\dot{E}=-\kappa E+gP,\quad \dot{P}=-\gamma _{\bot }P+gE\triangle , \quad \dot{\triangle }=-\gamma _{\Vert }(\triangle -\triangle _0)-4gPE,
\end{equation*}
where are real parameters. In addition, we prove this system is rationally non-integrable in the sense of Bogoyavlenskij for almost all parameter values
First integrals of the Maxwell–Bloch system
We investigate the analytic, rational and first integrals of the Maxwell–Bloch system
\begin{equation*}
\dot{E}=-\kappa E+gP,\quad \dot{P}=-\gamma _{\bot }P+gE\triangle , \quad \dot{\triangle }=-\gamma _{\Vert }(\triangle -\triangle _0)-4gPE,
\end{equation*}
where are real parameters. In addition, we prove this system is rationally non-integrable in the sense of Bogoyavlenskij for almost all parameter values