Voir la notice de l'article provenant de la source Cambridge University Press
Salem, Walid K. Abou; Sulem, Catherine. Resonant Tunneling of Fast Solitons through Large Potential Barriers. Canadian journal of mathematics, Tome 63 (2011) no. 6, pp. 1201-1219. doi: 10.4153/CJM-2011-029-6
@article{10_4153_CJM_2011_029_6,
author = {Salem, Walid K. Abou and Sulem, Catherine},
title = {Resonant {Tunneling} of {Fast} {Solitons} through {Large} {Potential} {Barriers}},
journal = {Canadian journal of mathematics},
pages = {1201--1219},
year = {2011},
volume = {63},
number = {6},
doi = {10.4153/CJM-2011-029-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-029-6/}
}
TY - JOUR AU - Salem, Walid K. Abou AU - Sulem, Catherine TI - Resonant Tunneling of Fast Solitons through Large Potential Barriers JO - Canadian journal of mathematics PY - 2011 SP - 1201 EP - 1219 VL - 63 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-029-6/ DO - 10.4153/CJM-2011-029-6 ID - 10_4153_CJM_2011_029_6 ER -
%0 Journal Article %A Salem, Walid K. Abou %A Sulem, Catherine %T Resonant Tunneling of Fast Solitons through Large Potential Barriers %J Canadian journal of mathematics %D 2011 %P 1201-1219 %V 63 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-029-6/ %R 10.4153/CJM-2011-029-6 %F 10_4153_CJM_2011_029_6
[1] Abou Salem, W. K., Effective dynamics of solitons in the presence of rough nonlinear perturbations. Nonlinearity 22(2009), no. 4, 747–763. doi:10.1088/0951-7715/22/4/004 Google Scholar
[2] Abou Salem, W. K., Solitary wave dynamics in time-dependent potentials. J. Math. Phys. 49(2008), no. 3, 032101. doi:10.1063/1.2837429 Google Scholar
[3] Abou Salem, W. K. and Sulem, C., Stochastic acceleration of solitons for the nonlinear Schrödinger equation. SIAM J. Math. Anal. 41(2009), no. 1, 117–152. doi:10.1137/080732419 Google Scholar
[4] Abou Salem, W. K., Fröhlich, J., and Sigal, I. M., Colliding solitons for the nonlinear Schrödinger equation. Commun. Math. Phys. 291(2009), no. 1, 151–176. doi:10.1007/s00220-009-0871-8 Google Scholar
[5] Abou Salem, W. K., Liu, X., and Sulem, C., Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation. Discrete Contin. Dyn. Syst (A) 29(2011), no. 4, 1637–1649. Google Scholar
[6] Bronski, J. C. and Jerrard, R. L., Soliton dynamics in a potential. Math. Res. Lett. 7(2000), no. 2–3, 329–342. Google Scholar
[7] Cazenave, T., Semilinear Schrödinger equations. Courant Lecture Notes in Mathematics, 10, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003. Google Scholar
[8] Fröhlich, J., Tsai, T.-P., and Yau, H.-T., On the point-particle (Newtonian) limit of the non-linear Hartree equation. Commun. Math. Phys. 225(2002), no. 2, 223–274. doi:10.1007/s002200100579 Google Scholar
[9] Fröhlich, J., Gustafson, S., Jonsson, B. L. G., and Sigal, I. M., Solitary wave dynamics in an external potential. Commun. Math. Phys. 250(2004), no. 3, 613–642. Google Scholar
[10] Fröhlich, J., Gustafson, S., Jonsson, B. L. G., and Sigal, I. M., Long time motion of NLS solitary waves in a confining potential. Ann. Henri Poincaré 7(2006), no. 4, 621–660. doi:10.1007/s00023-006-0263-y Google Scholar
[11] Ginibre, J. and Velo, G., On the class of nonlinear Schrödinger equations. II. Scattering theory, general case. J. Funct. Anal. 32(1979), no. 1, 33–71. doi:10.1016/0022-1236(79)90077-6 Google Scholar
[12] Golberg, M. and Schlag, W., Dispersive estimates for Schrödinger operators in dimensions one and three. Commun. Math. Phys. 251(2004), no. 1. 157–178. doi:10.1007/s00220-004-1140-5 Google Scholar
[13] Grillakis, M., Shatah, J., and Strauss, W., Stability theory of solitary waves in the presence of symmetry. I. J. Funct. Anal. 74(1987), no. 1, 160–197. doi:10.1016/0022-1236(87)90044-9 Google Scholar
[14] Holmer, J. and Zworski, M., Slow soliton interaction with delta impurities. J. Mod. Dyn. 1(2007), no. 4, 689–718. Google Scholar
[15] Holmer, J. and Zworski, M., Soliton interaction with slowly varying potentials. Int. Math. Res. Not. IMRN Art. ID rnn026. Google Scholar
[16] Holmer, J., Marzuola, J., and Zworski, M., Fast soliton scattering by delta impurities. Commun. Math. Phys. 274(2007), no. 1, 187–216. doi:10.1007/s00220-007-0261-z Google Scholar
[17] Journé, J.-L., Soffer, A., and Sogge, C. D., Decay estimates for Schrödinger operators. Comm. Pure Appl. Math. 44(1991), no. 5, 573–604. doi:10.1002/cpa.3160440504 Google Scholar
[18] Keel, M. and Tao, T., Endpoint Strichartz inequalities. Amer. J. Math. 120(1998), no. 5, 955–980. doi:10.1353/ajm.1998.0039 Google Scholar
[19] Reed, M. and Simon, B., Methods of modern mathematical physics. III. Scattering theory. Academic Press, New York-London, 1979. Google Scholar
[20] Rodnianski, I. and Schlag, W., Time decay for solutions of the Schrödinger equations with rough and time-dependent potentials. Invent. Math. 155(2004), no. 3, 451–513. doi:10.1007/s00222-003-0325-4 Google Scholar
[21] Strichartz, R. S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44(1977), no. 3, 705–714. doi:10.1215/S0012-7094-77-04430-1 Google Scholar
[22] Sulem, C. and Sulem, P.-L., The nonlinear Schrödinger equation. Self-focusing and wave collapse. Applied Mathematical Sciences, 139, Springer-Verlag, New York, 1999. Google Scholar
[23] Weder, R., Lp – Lp0 estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential. J. Funct. Anal. 170(2000), no. 1, 37–68. doi:10.1006/jfan.1999.3507 Google Scholar
Cité par Sources :