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Asymptotic behavior in time of solutions to complex-valued nonlinear Klein-Gordon equation in one space dimension. (English) Zbl 1473.35058

Summary: We consider the long time behavior of solutions to the initial value problem for the “complex-valued” cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the \(L^{\infty}\) decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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References:

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