Global attraction to solitary waves for Klein-Gordon equation with mean field interaction

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1. [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. Zbl0853.35112MR1199635
2. [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. Zbl0841.35108MR1334139
3. [3] Buslaev V.S., Sulem C., On asymptotic stability of solitary waves for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire20 (2003) 419-475. Zbl1028.35139MR1972870
4. [4] Cuccagna S., Asymptotic stability of the ground states of the nonlinear Schrödinger equation, Rend. Istit. Mat. Univ. Trieste32 (2001) 105-118, (2002), dedicated to the memory of Marco Reni. Zbl1006.35088MR1893394
5. [5] Cuccagna S., Stabilization of solutions to nonlinear Schrödinger equations, Comm. Pure Appl. Math.54 (2001) 1110-1145. Zbl1031.35129MR1835384
6. [6] Cuccagna S., On asymptotic stability of ground states of NLS, Rev. Math. Phys.15 (2003) 877-903. Zbl1084.35089MR2027616
7. [7] Komech A., On transitions to stationary states in one-dimensional nonlinear wave equations, Arch. Ration. Mech. Anal.149 (1999) 213-228. Zbl0939.35030MR1726676
8. [8] Komech A.I., Stabilization of the interaction of a string with a nonlinear oscillator, Moscow Univ. Math. Bull.46 (1991) 34-39. Zbl0784.35011MR1203302
9. [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. [10] Komech A.I., On stabilization of string-nonlinear oscillator interaction, J. Math. Anal. Appl.196 (1995) 384-409. Zbl0859.35076MR1359949
11. [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. Zbl1131.35003MR2308860
12. [12] Komech A., Spohn H., Long-time asymptotics for the coupled Maxwell–Lorentz equations, Comm. Partial Differential Equations25 (2000) 559-584. Zbl0970.35149MR1748357
13. [13] Komech A., Spohn H., Kunze M., Long-time asymptotics for a classical particle interacting with a scalar wave field, Comm. Partial Differential Equations22 (1997) 307-335. Zbl0878.35094MR1434147
14. [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. Zbl0863.35064MR1412428
15. [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. Zbl0228.35055MR303097
16. [16] Pillet C.-A., Wayne C.E., Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations, J. Differential Equations141 (1997) 310-326. Zbl0890.35016MR1488355
17. [17] Segal I.E., The global Cauchy problem for a relativistic scalar field with power interaction, Bull. Soc. Math. France91 (1963) 129-135. Zbl0178.45403MR153967
18. [18] Segal I.E., Non-linear semi-groups, Ann. of Math. (2)78 (1963) 339-364. Zbl0204.16004MR152908
19. [19] Soffer A., Weinstein M.I., Multichannel nonlinear scattering for nonintegrable equations, Commun. Math. Phys.133 (1990) 119-146. Zbl0721.35082MR1071238
20. [20] Soffer A., Weinstein M.I., Multichannel nonlinear scattering for nonintegrable equations. II. The case of anisotropic potentials and data, J. Differential Equations98 (1992) 376-390. Zbl0795.35073MR1170476
21. [21] Soffer A., Weinstein M.I., Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations, Invent. Math.136 (1999) 9-74. Zbl0910.35107MR1681113
22. [22] Strauss W.A., Decay and asymptotics for $\square u=f\left(u\right)$, J. Funct. Anal.2 (1968) 409-457. Zbl0182.13602MR233062
23. [23] Tao T., A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations, Dynam. Partial Differential Equations4 (2007) 1-53. Zbl1142.35088MR2304091