282 research outputs found
Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation
This paper obtains the dark, bright, dark-bright, dark-singular optical and singular soliton solutions to the nonlinear Schrödinger equation with quadratic-cubic nonlinearity (QC-NLSE), which describes the propagation of solitons through optical fibers. The adopted integration scheme is the sine-Gordon expansion method (SGEM). Further more, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis, and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNSE
Exact Solutions for Domain Walls in Coupled Complex Ginzburg - Landau Equations
The complex Ginzburg Landau equation (CGLE) is a ubiquitous model for the
evolution of slowly varying wave packets in nonlinear dissipative media. A
front (shock) is a transient layer between a plane-wave state and a zero
background. We report exact solutions for domain walls, i.e., pairs of fronts
with opposite polarities, in a system of two coupled CGLEs, which describe
transient layers between semi-infinite domains occupied by each component in
the absence of the other one. For this purpose, a modified Hirota bilinear
operator, first proposed by Bekki and Nozaki, is employed. A novel
factorization procedure is applied to reduce the intermediate calculations
considerably. The ensuing system of equations for the amplitudes and
frequencies is solved by means of computer-assisted algebra. Exact solutions
for mutually-locked front pairs of opposite polarities, with one or several
free parameters, are thus generated. The signs of the cubic gain/loss, linear
amplification/attenuation, and velocity of the coupled-front complex can be
adjusted in a variety of configurations. Numerical simulations are performed to
study the stability properties of such fronts.Comment: Journal of the Physical Society of Japan, in pres
Propagating Wave Patterns in a Derivative Nonlinear Schr\"odinger System with Quintic Nonlinearity
Exact expressions are obtained for a diversity of propagating patterns for a
derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These
patterns include bright pulses, fronts and dark solitons. The evolution of the
wave envelope is determined via a pair of integrals of motion, and reduction is
achieved to Jacobi elliptic cn and dn function representations. Numerical
simulations are performed to establish the existence of parameter ranges for
stability. The derivative quintic nonlinear Schr\"odinger model equations
investigated here are important in the analysis of strong optical signals
propagating in spatial or temporal waveguides.Comment: J. Phys. Soc. Jpn. in pres
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Anisotropic collapse in three-dimensional dipolar Bose-Einstein condensates
New extended generalized Kudryashov method for solving three nonlinear partial differential equations
New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics
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