Fast soliton scattering by delta impurities

Communications in Mathematical Physics

Volumn 274, Issue 1, 2007, Pages 187-216

  Holmer, Justin ^a   Marzuola, Jeremy ^a   Zworski, MacIej ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547337563     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0261-z     Document Type: Article

References (17)

1. Bronski, J.C., Jerrard, R.L.: Soliton dynamics in a potential. Math. Res. Lett. 7, 329-342 (2000)
2. Cao, X.D., Malomed, B.A.: Soliton-defect collisions in the nonlinear Schrödinger equation. Phys. Lett. A 206, 177-182 (1995)
3. Deift, P.A., Zhou, X.: Long-time asymptotics for solutions of the NLS equation with initial data in weighted Sobolev spaces. Comm. Pure Appl. Math. 56, 1029-1077 (2003)
4. Deift, P.A., Its, A.R., Zhou, X.: Long-time asymptotics for integrable nonlinear wave equations. In: Important developments in soliton theory, Springer Ser. Nonlinear Dynam., Berlin Springer, 1993 pp. 181-204
5. Faddeev, L.D., Takhtajan, L.A.: Hamiltonian Methods in the Theory of Solitons, Part One, Berlin Heidelberg New York: Springer Verlag, 1987
6. Floer, A., Weinstein, A.: Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. J. Funct. Anal. 69, 397-408 (1986)
7. Fröhlich, J., Gustafson, S., Jonsson, B.L.G., Sigal, I.M.: Solitary wave dynamics in an external potential. Commun. Math. Phys. 250, 613-642 (2005)
8. Goodman, R.H., Holmes, P.J., Weinstein, M.I.: Strong NLS soliton-defect interactions. Physica D 192, 215-248 (2004)
9. Holmer, J., Marzuola, J., Zworski, M.: Numerical study of soliton scattering by delta impurities. In preparation
10. Hörmander, L.: The Analysis of Linear Partial. Differential Operators, Vol.I,II. Berlin Heidelberg New York: Springer Verlag, 1983
11. Keel, M., Tao, T.: Endpoint Strichartz estimates. Amer. J. Math. 120, 955-980 (1998)
12. Kamvissis, S.: Long time behavior for the focusing nonlinear Schroedinger equation with real spectral singularities. Commun. Math. Phys. 180, 325-341 (1996)
13. Lax, P.D.: Integrals of nonlinear equations of evolution and solitary waves. Commun. Pure Appl. Math. 21, 467-490 (1968)
14. Maimistov, A.I., Basharov, M.: Nonlinear Optical Waves. Fundamental Theories of Physics 104, Dordrecht-Boston-London: Kluwer Academic Publishers 1999
15. Miles, J.W.: An envelope soliton problem. SIAM J. Appl. Math. 41(2), 227-230 (1981)
16. Tang, S.H., Zworski, M.: Potential scattering on the real line. Lecture notes, http://www.math.berkeley.edu/~zworski/tz1.pdf
17. Zakharov, V.E., Shabat, A.B.: Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Soviet Physics JETP 34(1), 62-69 (1972)