- Previous Article
- DCDS Home
- This Issue
-
Next Article
Global existence and uniqueness of a three-dimensional model of cellular electrophysiology
Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation
1. | Department of Mathematics, University of British Columbia, Vancouver, BC, Canada |
2. | Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada, Canada |
References:
[1] |
W. K. Abou Salem, Solitary wave dynamics in time-dependent potentials, J. Math. Phys., 49 (2008), 032101.
doi: 10.1063/1.2837429. |
[2] |
W. K. Abou Salem, Effective dynamics of solitons in the presence of rough nonlinear perturbations, Nonlinearity, 22 (2009), 747-763.
doi: 10.1088/0951-7715/22/4/004. |
[3] |
W. K. Abou Salem, J. Fröhlich and I. M. Sigal, Colliding solitons for the nonlinear Schrödinger equation, Commun. Math. Phys., 291 (2009), 151-176.
doi: 10.1007/s00220-009-0871-8. |
[4] |
W. K. Abou Salem and C. Sulem, Resonant tunneling of fast solitons through large potential barriers, to appear in Canad. J. Math., (2010). |
[5] |
G. D. Akrivis, V. A. Dougalis and O. A. Karakashian, On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation, Numerische Mathematik, 59 (1991), 31-53.
doi: 10.1007/BF01385769. |
[6] |
G. D. Akrivis, V. A. Dougalis, O. A. Karakashian and W. R. McKinney, Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrödinger equation, SIAM J. Sci. Comput., 25 (2003), 186-212.
doi: 10.1137/S1064827597332041. |
[7] |
J. C. Bronski and R. L. Jerrard, Soliton dynamics in a potential, Math. Res. Lett., 7 (2000), 329-342. |
[8] |
J. Fröhlich, S. Gustafson, B. L. G. Jonsson and I. M. Sigal, Solitary wave dynamics in an external potential, Commun. Math. Phys., 250 (2004), 613-642.
doi: 10.1007/s00220-004-1128-1. |
[9] |
J. Holmer and M. Zworski, Slow soliton interaction with delta impurities, J. Modern Dynamics, 1 (2007), 689-718. |
[10] |
J. Holmer and M. Zworski, Soliton interaction with slowly varying potentials, IMRN, (2008), ArtID 026, 36pp. |
[11] |
J. Holmer, J. Marzuola and M. Zworski, Fast soliton scattering by delta impurities, Commun. Math. Phys., 274 (2007), 187-216.
doi: 10.1007/s00220-007-0261-z. |
[12] |
J. Holmer, J. Marzuola and M. Zworski, Soliton splitting by external delta potentials, Journal of Nonlinear Science, 17 (2007), 349-367.
doi: 10.1007/s00332-006-0807-9. |
show all references
References:
[1] |
W. K. Abou Salem, Solitary wave dynamics in time-dependent potentials, J. Math. Phys., 49 (2008), 032101.
doi: 10.1063/1.2837429. |
[2] |
W. K. Abou Salem, Effective dynamics of solitons in the presence of rough nonlinear perturbations, Nonlinearity, 22 (2009), 747-763.
doi: 10.1088/0951-7715/22/4/004. |
[3] |
W. K. Abou Salem, J. Fröhlich and I. M. Sigal, Colliding solitons for the nonlinear Schrödinger equation, Commun. Math. Phys., 291 (2009), 151-176.
doi: 10.1007/s00220-009-0871-8. |
[4] |
W. K. Abou Salem and C. Sulem, Resonant tunneling of fast solitons through large potential barriers, to appear in Canad. J. Math., (2010). |
[5] |
G. D. Akrivis, V. A. Dougalis and O. A. Karakashian, On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation, Numerische Mathematik, 59 (1991), 31-53.
doi: 10.1007/BF01385769. |
[6] |
G. D. Akrivis, V. A. Dougalis, O. A. Karakashian and W. R. McKinney, Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrödinger equation, SIAM J. Sci. Comput., 25 (2003), 186-212.
doi: 10.1137/S1064827597332041. |
[7] |
J. C. Bronski and R. L. Jerrard, Soliton dynamics in a potential, Math. Res. Lett., 7 (2000), 329-342. |
[8] |
J. Fröhlich, S. Gustafson, B. L. G. Jonsson and I. M. Sigal, Solitary wave dynamics in an external potential, Commun. Math. Phys., 250 (2004), 613-642.
doi: 10.1007/s00220-004-1128-1. |
[9] |
J. Holmer and M. Zworski, Slow soliton interaction with delta impurities, J. Modern Dynamics, 1 (2007), 689-718. |
[10] |
J. Holmer and M. Zworski, Soliton interaction with slowly varying potentials, IMRN, (2008), ArtID 026, 36pp. |
[11] |
J. Holmer, J. Marzuola and M. Zworski, Fast soliton scattering by delta impurities, Commun. Math. Phys., 274 (2007), 187-216.
doi: 10.1007/s00220-007-0261-z. |
[12] |
J. Holmer, J. Marzuola and M. Zworski, Soliton splitting by external delta potentials, Journal of Nonlinear Science, 17 (2007), 349-367.
doi: 10.1007/s00332-006-0807-9. |
[1] |
Dario Bambusi, A. Carati, A. Ponno. The nonlinear Schrödinger equation as a resonant normal form. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 109-128. doi: 10.3934/dcdsb.2002.2.109 |
[2] |
Roy H. Goodman, Jeremy L. Marzuola, Michael I. Weinstein. Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 225-246. doi: 10.3934/dcds.2015.35.225 |
[3] |
Edès Destyl, Jacques Laminie, Paul Nuiro, Pascal Poullet. Numerical simulations of parity–time symmetric nonlinear Schrödinger equations in critical case. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2805-2821. doi: 10.3934/dcdss.2020411 |
[4] |
J. Colliander, M. Keel, Gigliola Staffilani, H. Takaoka, T. Tao. Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 665-686. doi: 10.3934/dcds.2008.21.665 |
[5] |
Liren Lin, Tai-Peng Tsai. Mixed dimensional infinite soliton trains for nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 295-336. doi: 10.3934/dcds.2017013 |
[6] |
Wentao Huang, Jianlin Xiang. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1309-1333. doi: 10.3934/cpaa.2016.15.1309 |
[7] |
Takahisa Inui. Global dynamics of solutions with group invariance for the nonlinear schrödinger equation. Communications on Pure and Applied Analysis, 2017, 16 (2) : 557-590. doi: 10.3934/cpaa.2017028 |
[8] |
D.G. deFigueiredo, Yanheng Ding. Solutions of a nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 563-584. doi: 10.3934/dcds.2002.8.563 |
[9] |
Hristo Genev, George Venkov. Soliton and blow-up solutions to the time-dependent Schrödinger-Hartree equation. Discrete and Continuous Dynamical Systems - S, 2012, 5 (5) : 903-923. doi: 10.3934/dcdss.2012.5.903 |
[10] |
Xiaobing Feng, Shu Ma. Stable numerical methods for a stochastic nonlinear Schrödinger equation with linear multiplicative noise. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 687-711. doi: 10.3934/dcdss.2021071 |
[11] |
José Luis López. A quantum approach to Keller-Segel dynamics via a dissipative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2601-2617. doi: 10.3934/dcds.2020376 |
[12] |
Shalva Amiranashvili, Raimondas Čiegis, Mindaugas Radziunas. Numerical methods for a class of generalized nonlinear Schrödinger equations. Kinetic and Related Models, 2015, 8 (2) : 215-234. doi: 10.3934/krm.2015.8.215 |
[13] |
M. D. Todorov, C. I. Christov. Conservative numerical scheme in complex arithmetic for coupled nonlinear Schrödinger equations. Conference Publications, 2007, 2007 (Special) : 982-992. doi: 10.3934/proc.2007.2007.982 |
[14] |
Pavel I. Naumkin, Isahi Sánchez-Suárez. On the critical nongauge invariant nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 807-834. doi: 10.3934/dcds.2011.30.807 |
[15] |
Tarek Saanouni. Remarks on the damped nonlinear Schrödinger equation. Evolution Equations and Control Theory, 2020, 9 (3) : 721-732. doi: 10.3934/eect.2020030 |
[16] |
Younghun Hong. Scattering for a nonlinear Schrödinger equation with a potential. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1571-1601. doi: 10.3934/cpaa.2016003 |
[17] |
Alexander Komech, Elena Kopylova, David Stuart. On asymptotic stability of solitons in a nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1063-1079. doi: 10.3934/cpaa.2012.11.1063 |
[18] |
Hongwei Wang, Amin Esfahani. On the Cauchy problem for a nonlocal nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022039 |
[19] |
W. Josh Sonnier, C. I. Christov. Repelling soliton collisions in coupled Schrödinger equations with negative cross modulation. Conference Publications, 2009, 2009 (Special) : 708-718. doi: 10.3934/proc.2009.2009.708 |
[20] |
Anna Maria Candela, Caterina Sportelli. Soliton solutions for quasilinear modified Schrödinger equations in applied sciences. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022121 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]