Geodesic
Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity
Yuan, Xu1
1 CMLS, École polytechnique, CNRS, Institut Polytechnique de Paris, F-91128 Palaiseau Cedex, France
Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1487-1524

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We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity

∂t2u−∂x2u+u−|u|p−1u+|u|q−1u=0,on[0,∞)×R,
where 1<q<p<∞. The main result states the stability in the energy space H1(R)×L2(R) 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.

DOI : 10.1016/j.anihpc.2020.11.008
Classification : 35L71, 35B35
Keywords: 1D nonlinear Klein-Gordon equation, Multi-solitons, Conditional stability

Yuan, Xu 1

1 CMLS, École polytechnique, CNRS, Institut Polytechnique de Paris, F-91128 Palaiseau Cedex, France 
@article{AIHPC_2021__38_5_1487_0,
     author = {Yuan, Xu},
     title = {Conditional stability of multi-solitons for the {1D} {NLKG} equation with double power nonlinearity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1487--1524},
     publisher = {Elsevier},
     volume = {38},
     number = {5},
     year = {2021},
     doi = {10.1016/j.anihpc.2020.11.008},
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     zbl = {1471.35034},
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Yuan, Xu. Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity. Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1487-1524. doi: 10.1016/j.anihpc.2020.11.008

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