Numerical studies of stabilized Townes solitons

Mathematics and Computers in Simulation

Volumn 69, Issue 5-6, 2005, Pages 447-456

  Montesinos, Gaspar D ^a   Pérez García, Víctor M ^a  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Blowup phenomena; Bose Einstein condensation; Nonlinear waves

Indexed keywords

CONDENSATION; FUNCTIONS; NUMERICAL ANALYSIS; PARAMETER ESTIMATION; PROBLEM SOLVING;

BLOWUP PHENOMENA; BOSE-EINSTEIN CONDENSATION; NONLINEAR WAVES; NONLINEARITY; SCHRONDINGER EQUATIONS; TOWNES SOLITONS;

SOLITONS;

EID: 23144437196     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2005.03.009     Document Type: Conference Paper

References (18)

1. C. Sulem, and P. Sulem The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse 2000 Springer Berlin
2. L. Vázquez L. Streit V.M. Pérez-García Nonlinear Klein-Gordon and Schrödinger Systems: Theory and Applications 1996 World Scientific Singapore
3. G. Fibich, and G. Papanicolaou Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension SIAM J. Appl. Math. 60 1999 183 240
4. M.I. Weinstein Non-linear Scrödinger-equations and sharp interpolation estimates Commun. Math. Phys. 87 1983 567 576
5. L. Berge, V.K. Mezentsev, J.J. Rasmussen, P.L. Christiansen, and Y.B. Gaididei Self-guiding light in layered nonlinear media Opt. Lett. 25 2000 1037 1039
6. I. Towers, and B.A. Malomed Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity J. Opt. Soc. Am. B 19 2002 537 543
7. A. Kaplan, B.V. Gisin, and B.A. Malomed Stable propagation and all-optical switching in planar waveguide-antiwaveguide periodic structures J. Opt. Soc. Am. B 19 2002 522 528
8. H. Saito, and M. Ueda Dynamically stabilized bright solitons in a two-dimensional Bose-Einstein condensate Phys. Rev. Lett. 90 2003 040403
9. F. Abdullaev, J.G. Caputo, R.A. Kraenkel, and B.A. Malomed Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length Phys. Rev. A 67 2003 013605
10. G.D. Montesinos, V.M. Pérez-García, and P. Torres Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers Physica D 191 2004 193 210
11. G.D. Montesinos, V.M. Pérez-García, and H. Michinel Stabilized two-dimensional vector solitons Phys. Rev. Lett. 92 2004 133901
12. P. Tran Solving the time-dependent Schrödinger equation: suppression of reflection from the grid boundary with a filtered split-operator approach Phys. Rev. E 58 1998 8049 8051
13. T. Fevens, and H. Jiang Absorbing boundary conditions for the Schrödinger equation SIAM J. Sci. Comput. 21 1999 255 282
14. T.R. Taha, M.J. Ablowitz, and Analytical numerical aspects of certain nonlinear evolution equations. 2. Numerical, nonlinear Schrödinger equation J. Comp. Phys. 1984 203 230
15. V.M. Pérez-García, and X. Liu Numerical methods for the simulation of trapped nonlinear Schrödinger systems Appl. Math. Comput. 144 2003 215 235
16. S. Blanes, and P.C. Moan Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nystrom methods J. Comp. Appl. Math. 142 2002 313 330
17. S. Cuccagna Stabilization of solutions to nonlinear Schrödinger equations Commun. Pure Appl. Math. 54 2001 1110 1145
18. T.P. Tsai, and H.T. Yau Asymptotic dynamics of nonlinear Schrödinger equations: resonance-dominated and dispersion-dominated solutions Commun. Pure Appl. Math. 55 2002 153 216