We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity
where . The main result states the stability in the energy space of the sums of decoupled solitary waves with different speeds, up to the natural instabilities. The proof is inspired by the techniques developed for the generalized Korteweg-de Vries equation and the nonlinear Schrödinger equation in a similar context by Martel, Merle and Tsai [14,15]. However, the adaptation of this strategy to a wave-type equation requires the introduction of a new energy functional adapted to the Lorentz transform.
Cite this article
Xu Yuan, Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 5, pp. 1487–1524DOI 10.1016/J.ANIHPC.2020.11.008