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• W2032035371 abstract "We employ global quasi-steady manifolds to rigorously reduce forced, linearly damped dispersive partial differential equations to finite dimensional flows. The manifolds we consider are not invariant, but through a renormalization group method we capture the long-time evolution of the full system as a flow on the manifold. For the parametric nonlinear Schrödinger equation we consider a manifold describing N well-separated pulses and derive an explicit system of ordinary differential equations for the flow on the manifold which captures the leading order pulse motion through the tail-tail interactions. We also outline a rigorous connection between the slow evolution in the hyperbolic PNLS and the fourth-order parabolic phase sensitive amplification equation for fiber optic systems." @default.
• W2032035371 created "2016-06-24" @default.
• W2032035371 creator A5024694851 @default.
• W2032035371 date "2002-01-01" @default.
• W2032035371 modified "2023-10-17" @default.
• W2032035371 title "A Renormalization Method for Modulational Stability of Quasi-Steady Patterns in Dispersive Systems" @default.
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• W2032035371 doi "https://doi.org/10.1137/s0036141000377547" @default.
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