Soliton scattering by delta impurities

Justin Holmer[1]; Jeremy Marzuola[1]; Maciej Zworski[1]

  • [1] Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA

Journées Équations aux dérivées partielles (2006)

  • Volume: 274, Issue: 1, page 1-6
  • ISSN: 0752-0360

How to cite

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Holmer, Justin, Marzuola, Jeremy, and Zworski, Maciej. "Soliton scattering by delta impurities." Journées Équations aux dérivées partielles 274.1 (2006): 1-6. <http://eudml.org/doc/10618>.

@article{Holmer2006,
affiliation = {Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA; Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA; Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA},
author = {Holmer, Justin, Marzuola, Jeremy, Zworski, Maciej},
journal = {Journées Équations aux dérivées partielles},
keywords = {delta function potential; quantum transmission rate; Gross-Pitaevskii equation; solitons},
language = {eng},
month = {6},
number = {1},
pages = {1-6},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Soliton scattering by delta impurities},
url = {http://eudml.org/doc/10618},
volume = {274},
year = {2006},
}

TY - JOUR
AU - Holmer, Justin
AU - Marzuola, Jeremy
AU - Zworski, Maciej
TI - Soliton scattering by delta impurities
JO - Journées Équations aux dérivées partielles
DA - 2006/6//
PB - Groupement de recherche 2434 du CNRS
VL - 274
IS - 1
SP - 1
EP - 6
LA - eng
KW - delta function potential; quantum transmission rate; Gross-Pitaevskii equation; solitons
UR - http://eudml.org/doc/10618
ER -

References

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  2. X.D. Cao and B.A. Malomed, Soliton-defect collisions in the nonlinear Schrödinger equation, Physics Letters A 206(1995), 177–182. Zbl1020.78505MR1369717
  3. P.A. Deift, A.R. Its, and X. Zhou, Long-time asymptotics for integrable nonlinear wave equations, in Important developments in soliton theory, 181–204, Springer Ser. Nonlinear Dynam., Springer, Berlin, 1993. Zbl0926.35132MR1280475
  4. L.D. Faddeev and L.A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Part One Springer Verlag, 1987. Zbl1111.37001MR905674
  5. A. Floer and A. Weinstein, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal. 69(1986), 397–408. Zbl0613.35076MR867665
  6. J. Frölich, S. Gustafson, B.L.G. Jonsson, and I.M. Sigal, Solitary wave dynamics in an external potential, Comm. Math. Physics, 250(2005), 613–642. Zbl1075.35075MR2094474
  7. R.H. Goodman, P.J. Holmes, and M.I. Weinstein, Strong NLS soliton-defect interactions, Physica D 192(2004), 215–248. Zbl1061.35132MR2065079
  8. J. Holmer, J. Marzuola, and M. Zworski, Fast soliton scattering by delta impurities, preprint 2006, math.AP/0602187. Zbl1126.35068
  9. J. Holmer, J. Marzuola, and M. Zworski, Numerical study of soliton scattering by delta impurities, in preparation. Zbl1126.35068
  10. S. Kamvissis, Long time behavior for the focusing nonlinear Schroedinger equation with real spectral singularities, Comm. Math. Phys. 180(1996), 325–341. Zbl0872.35101MR1405954
  11. V.E. Zakharov and A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP 34 (1972), no. 1, 62–69. MR406174

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