论文信息 - NUMERICAL METHODS FOR A COUPLED NONLINEAR SCHRÖDINGER SYSTEM

NUMERICAL METHODS FOR A COUPLED NONLINEAR SCHRÖDINGER SYSTEM

M. SEPULVEDA AND O. VERA† Departamento de Ingenieria Matematica, Universidad de Concepcion, Chile. †Departamento de Matematica, Universidad del Bio-Bio, Chile. We study a numerical method based on a Crank-Nicolson scheme for a coupled nonlinear Schrodinger system that describes some physical phenomena such as the propagation in birefringent optical fibers, Kerrlike photo refractive media in optics and Bose-Einstein condensates. This numerical scheme preserves the densities and the energy of the solution, and it is proved the convergence of its sequence of solutions. Key words: Schrodinger equations, asymptotically free solution, Crank- Nicolson scheme. AMS subject classifications: 35Q55, 35B40, 65N06

Mauricio Sepúlveda | M. Sepúlveda | O. V. Villagrán | Octavio Vera Villagrán

[1] Thierry Colin,et al. Semidiscretization in time for nonlinear Schrödinger-waves equations , 1998 .

[2] Ivan P. Kaminow,et al. Polarization in optical fibers , 1981 .

[3] Walter A. Strauss,et al. Nonlinear Scattering Theory , 1974 .

[4] Thierry Cazenave,et al. The Cauchy problem for the critical nonlinear Schro¨dinger equation in H s , 1990 .

[5] Hector D. Ceniceros. A semi-implicit moving mesh method for the focusing nonlinear Schrödinger equation , 2001 .

[6] R. Glassey. On the asymptotic behavior of nonlinear wave equations : blow-up theorems and applications to scattering theory , 1973 .

[7] J. Gillis,et al. Linear Differential Operators , 1963 .

[8] Michel C. Delfour,et al. Finite-difference solutions of a non-linear Schrödinger equation , 1981 .

[9] M. Sepúlveda,et al. Gain in regularity for a coupled nonlinear Schrödinger system , 2009 .

[10] E. S. P. Siqueira. Asymptotic behavior of the solutions of a nonlinear system of Schro¨dinger equations , 1993 .

[11] Christophe Besse,et al. A Relaxation Scheme for the Nonlinear Schrödinger Equation , 2004, SIAM J. Numer. Anal..

[12] B. Pellacci,et al. Positive solutions for a weakly coupled nonlinear Schrödinger system , 2006 .

[13] Curtis R. Menyuk,et al. Pulse propagation in an elliptically birefringent Kerr medium , 1989 .

[14] M. Sepúlveda,et al. On the nonexistence of asymptotically free solutions for a coupled nonlinear Schrödinger system , 2009 .