Monday, February 18, 2013

1302.3814 (Jacopo Bellazzini et al.)

Multi-solitary waves for the nonlinear Klein-Gordon equation    [PDF]

Jacopo Bellazzini, Marco Ghimenti, Stefan Le Coz
We consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates.
View original:

No comments:

Post a Comment