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Long-time decay for the linearized system of a charged particle in the Klein-Gordon field. (English) Zbl 1259.35175

Summary: We establish a long time decay for linearized dynamics of nonlinear Hamilton system which describes interaction of a charged particle with the Klein-Gordon field. The main contribution is deriving the decay for the frozen linearized system for initial data which are symplectic orthogonal to the root space of the linear differential operator involved.

MSC:

35Q51 Soliton equations
35Q70 PDEs in connection with mechanics of particles and systems of particles
35B40 Asymptotic behavior of solutions to PDEs
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Full Text: Euclid