Self-similar solutions and collective coordinate methods for nonlinear Schrödinger equations

Physica D: Nonlinear Phenomena

Volumn 191, Issue 3-4, 2004, Pages 211-218

  Pérez García, Víctor M ^a  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Collective coordinate methods; Nonlinear matter waves; Nonlinear optics; Nonlinear Schr dinger equations; Self similar solutions; Solitary waves; Time dependent variational method

Indexed keywords

DYNAMICS; LAGRANGE MULTIPLIERS; NONLINEAR OPTICS; WATER WAVES; WAVE PROPAGATION;

COLLECTIVE COORDINATE METHODS; NONLINEAR MATTER WAVES;

NONLINEAR EQUATIONS;

EID: 1842736760     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2003.12.010     Document Type: Article

References (25)

1. L. Vázquez, L. Streit, V.M. Pérez-García (Eds.), Nonlinear Klein-Gordon and Schrödinger Systems: Theory and Applications, World Scientific, Singapore, 1996.
2. C. Sulem, P. Sulem, The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse, Springer, Berlin, 2000.
3. Anderson M.H., Ensher J.R., Matthews M.R., Wieman C.E., Cornell E.A., Observation of Bose-Einstein condensation in a dilute atomic vapor. Science. 269:1995;198.
4. Davis K.B., Mewes M.O., Andrews M.R., Vandruten N.J., Durfee D.S., Kurn D.M., Ketterle W., Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75:1995;3969.
5. Cuccagna S., Stabilization of solutions to nonlinear Schrödinger equations. Comm. Pure Appl. Math. 54:2001;1110-1145.
6. Tsai T.P., Yau H.T., Asymptotic dynamics of nonlinear Schrödinger equations: resonance-dominated and dispersion-dominated solutions. Comm. Pure Appl. Math. 55:2002;153-216.
7. M.J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981.
8. García-Ripoll J.J., Pérez-García V.M., Torres P., Extended parametric resonances in nonlinear Schrödinger systems. Phys. Rev. Lett. 83:1999;1715.
9. Ghosh P.K., Exact results on the dynamics of a multicomponent Bose-Einstein condensate. Phys. Rev. A. 65:2002;053601.
10. V.M. Pérez-García, G.D. Montesinos, P. Torres, SIAM J. Appl. Math., 2003, in preparation.
11. Sánchez A., Bishop A.R., Collective coordinates and length-scale competition in spatially inhomogeneous soliton-bearing equations. SIAM Rev. 40:1999;579-615.
12. Malomed B.A., Variational methods in nonlinear fiber optics and related fields. Prog. Opt. 43:2002;69.
13. Oh Y., Cauchy problem and Ehrenfest's law of nonlinear Schrödinger equations with potentials. J. Diff. Eqn. 81:1989;255-274.
14. García-Ripoll J.J., Pérez-García V.M., Vekslerchik V., Construction of exact solutions by spatial translations in inhomogenous nonlinear Schrödinger equations. Phys. Rev. E. 64:2001;056602-1:6.
15. Berge L., Wave collapse in physics: principles and applications to light and plasma waves. Phys. Rep. 303:1998;259.
16. Fibich G., Papanicolau G., Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension. SIAM J. Appl. Math. 60:1999;183-240.
17. Pérez-García V.M., Michinel H., Cirac J.I., Lewenstein M., Zoller P., Dynamics of Bose-Einstein condensates: variational solutions of the Gross-Pitaevskii equations. Phys. Rev. A. 57:1997;1424.
18. Abdullaev F.K., Gammal A., Tomio L., Frederico T., Stability of trapped Bose-Einstein condensates. Phys. Rev. A. 63:2001;043604.
19. Gammal A., Frederico T., Tomio L., Abdullaev F.K., Stability analysis of the. D -dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions Phys. Lett. A. 267:2000;305-311.
20. Tomio L., Filho V.S., Gammal A., Frederico T., Stability of atomic condensed systems with attractive two-body interactions. Laser Phys. 13:2003;582-586.
21. Berge L., Mezentsev V.K., Rasmussen J.J., Christiansen P.L., Gaididei Y.B., Self-guiding light in layered nonlinear media. Opt. Lett. 25:2000;1037-1039.
22. Towers I., Malomed B.A., Stable. (2+1) -dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity J. Opt. Soc. Am. B. 19:2002;537-543.
23. Kaplan A., Gisin B.V., Malomed B.A., Stable propagation and all-optical switching in planar waveguide-antiwaveguide periodic structures. J. Opt. Soc. Am. B. 19:2002;522-528.
24. Abdullaev F., Caputo J.G., Kraenkel R.A., Malomed B.A., Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A. 67:2003;013605.
25. G.D. Montesinos, V.M. Pérez-García, P. Torres, Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers, Physica D 191 (2004) 193-210.