Lie group symmetry classification of solutions to coupled nonlinear Schrodinger equations

By applying the Lie group reduction method a full symmetry classification of one parameter group invariant solutions of two coupled nonlinear Schrodinger equations is presented. The physical situations under consideration include propagation of two polarization modes in weak and strong birefringent fibers, propagation of two waves at different carrier wavelengths, and nonlinear directional couplers.

[1]  I. Uzunov,et al.  New kinds of periodical waves in birefringent optical fibers , 1992 .

[2]  Paré,et al.  Approximate model of soliton dynamics in all-optical couplers. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[3]  R. Tremblay,et al.  Periodic and solitary waves in bimodal optical fibres , 1989 .

[4]  D. Christodoulides,et al.  Vector solitons in birefringent nonlinear dispersive media. , 1988, Optics letters.

[5]  I. Uzunov,et al.  Solutions and laws of conservation for coupled nonlinear Schrodinger equations: Lie group analysis , 1998 .

[6]  G. Stegeman,et al.  Soliton switching in fiber nonlinear directional couplers. , 1988, Optics letters.

[7]  Antonello Cutolo,et al.  Coupled-mode theory of nonlinear propagation in multimode and single-mode fibers: envelope solitons and self-confinement , 1982 .

[8]  Sipe,et al.  Bound solitary waves in a birefringent optical fiber. , 1988, Physical review. A, General physics.

[9]  B. M. Fulk.  MATH , 1992 .

[10]  P. Olver.  Applications of Lie Groups to Differential Equations , 1986 .

[11]  Leo,et al.  Symmetry properties and exact patterns in birefringent optical fibers. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  R. Tremblay,et al.  Symbiotic periodic waves in a nonlinear birefringent fiber , 1994 .

[13]  D. Christodoulides.  Black and white vector solitons in weakly birefringent optical fibers , 1988 .

[14]  Lederer,et al.  Pulse switching in nonlinear fiber directional couplers. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.