We prove that the short-pulse equation, which is derived from a quasilinear Klein–Gordon equation with formal asymptotic methods, can be rigorously justified. The justification procedure applies to small-norm solutions of the short-pulse equation. Although the small-norm solutions exist for infinite times and include modulated pulses and their elastic interactions, the error bound for arbitrary...

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

We prove the global well-posedness and we study the linear response for a system of two coupled equations composed of a Dirac equation for an infinite rank operator and a nonlinear wave or Klein-Gordon equation.

We prove that small smooth solutions of semi-linear Klein-Gordon equations with quadratic potential exist over a longer interval than the one given by local existence theory, for almost every value of mass. We use normal form for the Sobolev energy. The difficulty in comparison with some similar results on the sphere comes from the fact that two successive eigenvalues λ, λ′ of √ −∆+ |x|2 may be...