An Energy Equation for the Weakly Damped Driven Nonlinear Schrödinger Equations and its Application to their Attractors
In this note we present an energy equation concerning the H2 norm of a forced one-dimensional nonlinear Schrödinger equation. as an application we are able to corroborate recent results on attractors of weakly damped forced nonlinear Schrödinger equation, by proving that the attractor is an attractor in the strong topology of H2 and its Hausdorff and fractal dimensions are finite in H2. the energy equation for the H1 norm can be derived in the same fashion and it implies corresponding results for the attractor in H1. © 1995.
X. Wang, "An Energy Equation for the Weakly Damped Driven Nonlinear Schrödinger Equations and its Application to their Attractors," Physica D: Nonlinear Phenomena, vol. 88, no. 3 thru 4, pp. 167 - 175, Elsevier, Dec 1995.
The definitive version is available at https://doi.org/10.1016/0167-2789(95)00196-B
Mathematics and Statistics
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01 Dec 1995