Solution interaction with slowly varying potentials

International Mathematics Research Notices

Volumn 2008, Issue 1, 2008, Pages

  Holmer, Justin ^a   Zworski, Maciej ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67650756865     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1093/imrn/rnn026     Document Type: Article

References (14)

1. Abou Salem, W. K. "Solitary wave dynamics in time-dependent potentials." (2007): preprint, arXiv:0707.0272.
2. Bronski, J. C., and R. L. Jerrard. "Soliton dynamics in a potential." Mathematical Research Letters 1 (2000): 329-12.
3. Carles, R., and L. Miller. "Semiclassical nonlinear Schrödinger equations with potential and focusing initial data." Osaka Journal of Mathematics 41 (2004): 693-725. (Pubitemid 39620594)
4. Eboli, O. J. P., and G. C. Marques. "Solitons as Newtonian particles." Physical Review B 28 (1983): 689-96.
5. Floer, A., and A. Weinstein. "Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential." Journal of Functional Analysis 69 (1986): 397-408.
6. Fröhlich, J., S. Gustafson, B. L. G. Jonsson, and I. M. Sigal. "Solitary wave dynamics in an external potential." Communications in Mathematical Physics 250 (2004): 613-42. (Pubitemid 39436333)
7. Fröhlich, J., S. Gustafson, B. L. G. Jonsson, and I. M. Sigal. "Long time motion of NLS solitary waves in a confining potential." Annales Henri Poincaré 1 (2006): 621-60. (Pubitemid 43910312)
8. Fröhlich, J., T.-P. Tsai, and H.-T, Yau, "On the point-particle (Newtonian) limit of the nonlinear Hartree equation." Communications in Mathematical Physics 225 (2002): 223-74. (Pubitemid 40830984)
9. Holmer, J., J. Marzuola, and M. Zworski. "Fast soliton scattering by delta impurities." Communications in Mathematical Physics 274 (2007): 187-216.
10. Holmer, J., J. Marzuola, and M. Zworski, "Soliton splitting by delta impurities." Journal of Nonlinear Science 1 (2007): 349-67.
11. Holmer, J., and M. Zworski. "Slow soliton interaction with external delta potentials." Journal of Modern Dynamics 1, no. 4 (2007): 689-718. (Pubitemid 47128298)
12. Keraani, S. "Semiclassical limit of a class of Schrödinger equations with potential." Communications in Partial Differential Equations 27 (2002): 693-704.
13. Oh, Y. G. "On positive multi-lump bound states of nonlinear Schrödinger equations under multiple-well potentials." Communications in Mathematical Physics 131 (1990): 223-53.
14. Weinstein, M. I. "Lyapunov stability of ground states of nonlinear dispersive evolution equations." Communications on Pure and Applied Mathematics 29 (1986): 51-68.