Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity

Abstract

We consider the one-dimensional nonlinear Klein-Gordon equation with double power focusing-defocusing nonlinearityThe main result concerns the stability of the sum of several solitary waves with different speeds in the energy space H 1 (R)×L 2 (R), up to the natural instabilities. The proof involves techniques developed by Martel, Merle and Tsai [12,13] for the generalized KdV and NLS equations.In particular, we rely on an energy method and virial type estimates.