Effective Dynamics of the Vector Nonlinear Schr\"odinger Equations on Large Domains

Katherine Zhiyuan Zhang

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Effective Dynamics of the Vector Nonlinear Schr\"odinger Equations on Large Domains

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arxiv 2201.00861 v1 pith:DEJOPWZ5 submitted 2022-01-03 math.AP math.CA

Effective Dynamics of the Vector Nonlinear Schr\"odinger Equations on Large Domains

Katherine Zhiyuan Zhang This is my paper

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keywords largecontinuousdynamicseffectiveequationequationsnonlinearodinger

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We consider the vector nonlinear Schr\"odinger equation posed on the box with periodic boundary conditions, and derive the continuous resonant (CR) equation that describes the effective dynamics for large box size and small data size over very large time-scales. Moreover, we investigate various properties of the continuous resonant equations, including the Hamiltonian structure and the well-posedness, etc..

Effective Dynamics of the Vector Nonlinear Schr\"odinger Equations on Large Domains

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