Global Attraction to Solitary Waves for Klein-Gordon Equation With Mean Field Interaction
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, p. 855-868
@article{AIHPC_2009__26_3_855_0,
author = {Komech, Alexander and Komech, Andrew},
title = {Global Attraction to Solitary Waves for Klein-Gordon Equation With Mean Field Interaction},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {26},
number = {3},
year = {2009},
pages = {855-868},
doi = {10.1016/j.anihpc.2008.03.005},
zbl = {1177.35201},
mrnumber = {2526405},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2009__26_3_855_0}
}

Komech, Alexander; Komech, Andrew. Global Attraction to Solitary Waves for Klein-Gordon Equation With Mean Field Interaction. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, pp. 855-868. doi : 10.1016/j.anihpc.2008.03.005. http://www.numdam.org/item/AIHPC_2009__26_3_855_0/

[1] Buslaev V. S., Perel'Man G. S., Scattering for the Nonlinear Schrödinger Equation: States That Are Close to a Soliton, St. Petersburg Math. J. 4 (1993) 1111-1142. | MR 1199635 | Zbl 0853.35112

[2] Buslaev V. S., Perel'Man G. S., On the Stability of Solitary Waves for Nonlinear Schrödinger Equations, in: Nonlinear Evolution Equations, Amer. Math. Soc. Transl. Ser. 2, vol. 164, Amer. Math. Soc., Providence, RI, 1995, pp. 75-98. | MR 1334139 | Zbl 0841.35108

[3] Buslaev V. S., Sulem C., On Asymptotic Stability of Solitary Waves for Nonlinear Schrödinger Equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003) 419-475. | Numdam | MR 1972870 | Zbl 1028.35139

[4] Cuccagna S., Asymptotic Stability of the Ground States of the Nonlinear Schrödinger Equation, Rend. Istit. Mat. Univ. Trieste 32 (2001) 105-118, (2002), dedicated to the memory of Marco Reni. | MR 1893394 | Zbl 1006.35088

[5] Cuccagna S., Stabilization of Solutions to Nonlinear Schrödinger Equations, Comm. Pure Appl. Math. 54 (2001) 1110-1145. | MR 1835384 | Zbl 1031.35129

[6] Cuccagna S., On Asymptotic Stability of Ground States of NLS, Rev. Math. Phys. 15 (2003) 877-903. | MR 2027616 | Zbl 1084.35089

[7] Komech A., On Transitions to Stationary States in One-Dimensional Nonlinear Wave Equations, Arch. Ration. Mech. Anal. 149 (1999) 213-228. | MR 1726676 | Zbl 0939.35030

[8] Komech A. I., Stabilization of the Interaction of a String With a Nonlinear Oscillator, Moscow Univ. Math. Bull. 46 (1991) 34-39. | MR 1203302 | Zbl 0784.35011

[9] A.I. Komech, A.A. Komech, On global attraction to quantum stationary states II. Several nonlinear oscillators coupled to massive scalar field, MPI MIS Leipzig preprint 17/2007, 2007.

[10] Komech A. I., On Stabilization of String-Nonlinear Oscillator Interaction, J. Math. Anal. Appl. 196 (1995) 384-409. | MR 1359949 | Zbl 0859.35076

[11] Komech A. I., Komech A. A., Global Attractor for a Nonlinear Oscillator Coupled to the Klein-Gordon Field, Arch. Ration. Mech. Anal. 185 (2007) 105-142. | MR 2308860 | Zbl 1131.35003

[12] Komech A., Spohn H., Long-Time Asymptotics for the Coupled Maxwell-Lorentz Equations, Comm. Partial Differential Equations 25 (2000) 559-584. | MR 1748357 | Zbl 0970.35149

[13] Komech A., Spohn H., Kunze M., Long-Time Asymptotics for a Classical Particle Interacting With a Scalar Wave Field, Comm. Partial Differential Equations 22 (1997) 307-335. | MR 1434147 | Zbl 0878.35094

[14] Komech A. I., Vainberg B., On Asymptotic Stability of Stationary Solutions to Nonlinear Wave and Klein-Gordon Equations, Arch. Ration. Mech. Anal. 134 (1996) 227-248. | MR 1412428 | Zbl 0863.35064

[15] Morawetz C. S., Strauss W. A., Decay and Scattering of Solutions of a Nonlinear Relativistic Wave Equation, Comm. Pure Appl. Math. 25 (1972) 1-31. | MR 303097 | Zbl 0228.35055

[16] Pillet C.-A., Wayne C. E., Invariant Manifolds for a Class of Dispersive, Hamiltonian, Partial Differential Equations, J. Differential Equations 141 (1997) 310-326. | MR 1488355 | Zbl 0890.35016

[17] Segal I. E., The Global Cauchy Problem for a Relativistic Scalar Field With Power Interaction, Bull. Soc. Math. France 91 (1963) 129-135. | Numdam | MR 153967 | Zbl 0178.45403

[18] Segal I. E., Non-Linear Semi-Groups, Ann. of Math. (2) 78 (1963) 339-364. | MR 152908 | Zbl 0204.16004

[19] Soffer A., Weinstein M. I., Multichannel Nonlinear Scattering for Nonintegrable Equations, Commun. Math. Phys. 133 (1990) 119-146. | MR 1071238 | Zbl 0721.35082

[20] Soffer A., Weinstein M. I., Multichannel Nonlinear Scattering for Nonintegrable Equations. II. the Case of Anisotropic Potentials and Data, J. Differential Equations 98 (1992) 376-390. | MR 1170476 | Zbl 0795.35073

[21] Soffer A., Weinstein M. I., Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations, Invent. Math. 136 (1999) 9-74. | MR 1681113 | Zbl 0910.35107

[22] Strauss W. A., Decay and Asymptotics for $\square u=f\left(u\right)$, J. Funct. Anal. 2 (1968) 409-457. | MR 233062 | Zbl 0182.13602

[23] Tao T., A (Concentration-)Compact Attractor for High-Dimensional Non-Linear Schrödinger Equations, Dynam. Partial Differential Equations 4 (2007) 1-53. | MR 2304091 | Zbl 1142.35088