Soliton solution for an inhomogeneous highly dispersive media with a dual-power nonlinearity law

Optical soliton propagation in an inhomogeneous highly dispersive media with a dual-power nonlinearity law is studied. The variable-coefficient nonlinear Schrödinger (NLS) equation describing the propagation in such media includes space-dependent coefficients of fourth-order dispersion, cubic–quintic nonlinearity, and attenuation. By means of a solitary wave ansatz, exact bright soliton solution is found. Importantly, we have found that it is always possible to express the propagation of bright soliton pulses, for any integer value of the exponent in the power law in the form of a power of hyperbolic secant function. All physical parameters in the soliton solution are obtained as a function of the space-dependent model coefficients. Note that, it is always useful and desirable to construct exact analytical solutions for the understanding of most nonlinear physical phenomena.

[1]  E. Dianov,et al.  Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation , 1989 .

[2]  David Yevick,et al.  A numerical procedure for soliton generation , 1995 .

[3]  Yehuda B. Band,et al.  Optical Solitary Waves in the Higher Order Nonlinear Schrödinger Equation , 1996, patt-sol/9612004.

[4]  Zhou Xian-chu,et al.  Numerical simulation of standing solitons and their interaction , 2000 .

[5]  S. L. Palacios,et al.  Black optical solitons for media with parabolic nonlinearity law in the presence of fourth order dispersion , 2000 .

[6]  Jongbae Kim,et al.  A Coupled Higher‐Order Nonlinear Schrödinger Equation Including Higher‐Order Bright and Dark Solitons , 2001 .

[7]  Ildar R Gabitov,et al.  Shedding and interaction of solitons in imperfect medium , 2001 .

[8]  Woo-Pyo Hong,et al.  Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic non-Kerr terms , 2001 .

[9]  S. L. Palacios,et al.  Optical solitons in highly dispersive media with a dual-power nonlinearity law , 2003 .

[10]  Guosheng Zhou,et al.  Modulation instability and solitons on a cw background in inhomogeneous optical fiber media , 2004 .

[11]  戴朝卿,et al.  Bright and dark optical solitons in the nonlinear SchrSdinger equation with fourth-order dispersion and cubic-quintic nonlinearity , 2005 .

[12]  Thomas Frisch,et al.  Peeling off an elastica from a smooth attractive substrate. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Guosheng Zhou,et al.  Combined solitary wave solutions for the inhomogeneous higher-order nonlinear Schrodinger equation. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  A. Yariv,et al.  Perfect optical solitons : spatial Kerr solitons as exact solutions of Maxwell's equations , 2004, physics/0410257.

[15]  Elçin Yusufoglu,et al.  Solitons and periodic solutions of coupled nonlinear evolution equations by using the sine–cosine method , 2006, Int. J. Comput. Math..

[16]  M. A. Abdou,et al.  New solitons and periodic wave solutions for nonlinear evolution equations , 2006 .

[17]  Guosheng Zhou,et al.  Chirped soliton-like solutions for nonlinear Schrödinger equation with variable coefficients , 2006 .

[18]  D. Ch. Kim,et al.  On the theory of acoustic solitons in a liquid with distributed gas bubbles , 2007 .

[19]  K Aravinthan,et al.  A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation , 2007 .

[20]  Jaap I. Dijkhuis,et al.  Acoustic solitons in semiconductor nanostructures , 2007 .

[21]  Abdul-Majid Wazwaz,et al.  New solitons and kink solutions for the Gardner equation , 2007 .

[22]  Cleofé Campos-Pozuelo,et al.  Solitons in Water-air Mixtures: Solution of the Acoustic - bubble Vibration Coupling System , 2008 .

[23]  R. Sabry,et al.  New exact solutions for a generalized variable-coefficient KdV equation , 2008 .

[24]  Anjan Biswas,et al.  1-soliton solution of (1 + 2)-dimensional nonlinear Schrödinger's equation in dual-power law media , 2008 .

[25]  D. Ch. Kim.  Physical nature of acoustical solitons in liquid with distributed gas bubbles , 2008 .

[26]  Qun Lin,et al.  Linear B-spline finite element method for the improved Boussinesq equation , 2009 .