Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Approximately invariant elliptic slow manifolds are constructed for the Lorenz-Krishnamurthy model of fast-slow interactions in the atmosphere. As is the case for many other two-time-scale systems, the various asymptotic procedures that may be used for this construction diverge, and there are no exactly invariant slow manifolds. Valuable information can hover be gained by cap- turing the details of the divergence: this makes it possible to define exponentially accurate slow manifolds, identify one of these as optimal, and predict the amplitude and phase of the fast oscilla- tions that appear for trajectories started on it.  demonstrate this for the Lorenz-Krishnamurthy model by studying the slow manifolds obtained using a por-series expansion procedure.  de- velop two distinct methods to derive the leading-order asymptotics of the late coefficients in this expansion. Borel summation is then used to define a unique slow manifold, regarded as optimal, which is piecewise analytic in the slow variables. This slow manifold is not analytic on a Stokes surface: when slow solutions cross this surface, they switch on exponentially small fast oscillations through a Stokes phenomenon.  show that the form of these oscillations can be recovered from the Borel summation. The approach that  develop for the Lorenz-Krishnamurthy model has a general applicability;  sketch how it generalizes to a broad class of two-time-scale systems.
['Jacques Vanneste']
I am writing a research paper on a idea Asymptotics of a Slow Manifold
[{"from": "human", "value": "I am writing a research paper on a idea Asymptotics of a Slow Manifold"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Approximately invariant elliptic slow manifolds are constructed for the Lorenz-Krishnamurthy model of fast-slow interactions in the atmosphere. As is the case for many other two-time-scale systems, the various asymptotic procedures that may be used for this construction diverge, and there are no exactly invariant slow manifolds. Valuable information can hover be gained by cap- turing the details of the divergence: this makes it possible to define exponentially accurate slow manifolds, identify one of these as optimal, and predict the amplitude and phase of the fast oscilla- tions that appear for trajectories started on it.  demonstrate this for the Lorenz-Krishnamurthy model by studying the slow manifolds obtained using a por-series expansion procedure.  de- velop two distinct methods to derive the leading-order asymptotics of the late coefficients in this expansion. Borel summation is then used to define a unique slow manifold, regarded as optimal, which is piecewise analytic in the slow variables. This slow manifold is not analytic on a Stokes surface: when slow solutions cross this surface, they switch on exponentially small fast oscillations through a Stokes phenomenon.  show that the form of these oscillations can be recovered from the Borel summation. The approach that  develop for the Lorenz-Krishnamurthy model has a general applicability;  sketch how it generalizes to a broad class of two-time-scale systems."}]