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Hamiltonian dynamics of a particle interacting with a wave field. (English) Zbl 1281.35084

Summary: We study the Hamiltonian equations of motion of a heavy tracer particle interacting with a dense weakly interacting Bose-Einstein condensate in the classical (mean-field) limit. Solutions describing ballistic subsonic motion of the particle through the condensate are constructed. We establish asymptotic stability of ballistic subsonic motion.

MSC:

35Q70 PDEs in connection with mechanics of particles and systems of particles
35B35 Stability in context of PDEs
70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics
35B40 Asymptotic behavior of solutions to PDEs
35C07 Traveling wave solutions
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References:

[1] DOI: 10.3934/dcdsb.2010.13.537 · Zbl 1191.35041
[2] DOI: 10.1007/978-3-642-16830-7 · Zbl 1227.35004
[3] DOI: 10.1512/iumj.2008.57.3632 · Zbl 1171.35012
[4] Béthuel F., Annales de l’I.H.P. A 70 pp 147238– (1999)
[5] Boboliubov N.N., J. Phys. (U. S. S. R.) 11 pp 23– (1947)
[6] DOI: 10.1007/s00220-002-0689-0 · Zbl 1073.37079
[7] DOI: 10.1007/BF02364705 · Zbl 0836.35146
[8] DOI: 10.1016/S0294-1449(02)00018-5 · Zbl 1028.35139
[9] DOI: 10.1002/cpa.1018 · Zbl 1031.35129
[10] DOI: 10.1063/1.4757278 · Zbl 1331.82031
[11] Fröhlich J., Annales de l’inst. Henri Poincaré 19 pp 1– (1974)
[12] DOI: 10.1063/1.3619799 · Zbl 1272.70067
[13] DOI: 10.1007/s00220-012-1564-2 · Zbl 1263.82033
[14] DOI: 10.1007/s002200100579 · Zbl 1025.81015
[15] Gelfand I.M., Generalized Functions (1964)
[16] DOI: 10.1016/j.matpur.2008.09.009 · Zbl 1232.35152
[17] DOI: 10.1007/s00220-003-0961-y · Zbl 1044.35087
[18] DOI: 10.1016/0022-1236(87)90044-9 · Zbl 0656.35122
[19] DOI: 10.4310/MRL.2006.v13.n2.a8 · Zbl 1119.35084
[20] DOI: 10.1142/S0219199709003491 · Zbl 1180.35481
[21] DOI: 10.1016/S0375-9601(01)00197-9 · Zbl 01608339
[22] DOI: 10.1137/070711189 · Zbl 1167.35518
[23] Maris M., Journées Équations aux Déerivés Partielles pp 1– (2010)
[24] DOI: 10.1088/0951-7715/11/5/007 · Zbl 0910.35116
[25] DOI: 10.1007/s00023-003-0136-6 · Zbl 1057.81024
[26] DOI: 10.1137/S0036141094267522 · Zbl 0861.35013
[27] DOI: 10.1007/BF02096557 · Zbl 0721.35082
[28] DOI: 10.1016/0022-0396(92)90098-8 · Zbl 0795.35073
[29] Sulem C., The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (1999) · Zbl 0928.35157
[30] Tao T., Nonlinear Dispersive Equations: Local and Global Analysis (2006) · Zbl 1106.35001
[31] Volpert A.I., Traveling Wave Solutions of Parabolic Systems (1994) · Zbl 1017.34014
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