For the cubic nonlinear Klein-Gordon equation in the non-relativistic limit, the solution is approximated up to L² error ε⁴+(ε²t)^{α/4} by a first Schrödinger profile plus an ε² correction, for H^α data with α∈[4,8].
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High-order asymptotic expansion for the nonlinear Klein-Gordon equation in the non-relativistic limit regime
For the cubic nonlinear Klein-Gordon equation in the non-relativistic limit, the solution is approximated up to L² error ε⁴+(ε²t)^{α/4} by a first Schrödinger profile plus an ε² correction, for H^α data with α∈[4,8].