Extended modulational instability and new type of solitary wave in coupled nonlinear Schrödinger equations

Abstract We investigate the dynamics of the incoherently coupled nonlinear Schrodinger equations describing the propagation of two waves interacting through a third order nonlinearity. We show that the phenomenon of extended modulational instability induced by incoherent coupling is associated with the existence of a new type of solitary wave. This solitary wave consists of a bound state of two interacting semi-infinite symmetric kink waves.

[1]  D. McLaughlin,et al.  A modal representation of chaotic attractors for the driven, damped pendulum chain , 1990 .

[2]  A. Hasegawa.  Plasma instabilities and nonlinear effects , 1975 .

[3]  Wabnitz,et al.  Modulational polarization instability of light in a nonlinear birefringent dispersive medium. , 1988, Physical review. A, General physics.

[4]  E. Infeld,et al.  Quantitive theory of the Fermi-Pasta-Ulam recurrence in the nonlinear Schroedinger equation , 1981 .

[5]  Darryl D. Holm,et al.  Hamiltonian chaos in nonlinear optical polarization dynamics , 1990 .

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

[7]  S. Wabnitz,et al.  Low dimensional modulational chaos in diffractive nonlinear cavities , 1992 .

[8]  S. Wabnitz,et al.  Nonlinear modulation of coupled waves in birefringent optical fibers , 1991 .

[9]  Agrawal,et al.  Modulation instability induced by cross-phase modulation. , 1987, Physical review letters.

[10]  S Wabnitz,et al.  Dynamics of the nonlinear modulational instability in optical fibers. , 1991, Optics letters.

[11]  T. Brooke Benjamin,et al.  The disintegration of wave trains on deep water Part 1. Theory , 1967, Journal of Fluid Mechanics.

[12]  G. Stegeman,et al.  Polarized soliton instability and branching in birefringent fibers , 1989 .

[13]  K. Das,et al.  Modulational instability of two transverse waves in a cold plasma , 1979, Journal of Plasma Physics.

[14]  N. Akhmediev,et al.  Exact first-order solutions of the nonlinear Schrödinger equation , 1987 .

[15]  Stefano Trillo,et al.  Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects , 1991 .

[16]  V. Mezentsev,et al.  Magnetooptical solutons and simultons , 1988 .