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

top

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

top
  1. J. C. Bronski and R. L. Jerrard, Soliton dynamics in a potential, Math. Res. Lett. 7(2000), 329-342. Zbl0955.35067MR1764326
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.