From nonlinear Klein-Gordon equation to a system of coupled nonlinear Schrodinger equations

摘要

We show that the solutions for the nonlinear Klein-Gordon equation can be described by using a system of two coupled nonlinear Schrodinger equations as the speed of light tends to infinity, in the strong topology of the energy space. Each solution of the two Schrodinger equations corresponds to a distinct mode of oscillation in time. We can also give a finer description in the case where one of them vanishes. [References: 19]