Direct perturbation theory for the dark soliton solution to the nonlinear Schrödinger equation with normal dispersion

2007 ◽  
Vol 75 (4) ◽  
Author(s):  
Jia-Lu Yu ◽  
Chun-Nuan Yang ◽  
Hao Cai ◽  
Nian-Ning Huang
Keyword(s):  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Normal Dispersion ◽  
Nonlinear Schrödinger ◽  
Direct Perturbation

AN ALTERNATIVE SET OF BRIGHT AND DARK SOLITON SOLUTIONS OF THE NONLINEAR SCHRÖDINGER EQUATION

2001 ◽  
Vol 10 (04) ◽  
pp. 403-407 ◽  
Author(s):  
S. L. PALACIOS
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Normal Dispersion ◽  
Nonlinear Schrödinger ◽  
Dispersion Regime ◽  
Alternative Set

An alternative set of soliton solutions for the nonlinear Schrödinger equation is found. When particular cases are analyzed it is shown that bright picosecond solitons are possible in the normal and anomalous dispersion regions of an optical fibre but dark picosecond solitons can only exist in the normal dispersion regime. Also, pulse peak power and width are determined.

EXACT DARK SOLITON SOLUTION OF THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION

2009 ◽  
Vol 23 (24) ◽  
pp. 2869-2888 ◽  
Author(s):  
YI ZHANG ◽  
XIAO-NA CAI ◽  
CAI-ZHEN YAO ◽  
HONG-XIAN XU
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Generalized Nonlinear Schrödinger Equation ◽  
Hirota Bilinear

The generalized nonlinear Schrödinger equation with the variable coefficient is discussed, and the exact dark N-soliton solution is presented by using the Hirota bilinear method, from finding the 1-soliton to 2-soliton, and then we obtain the N-soliton solution. With the aid of Maple, a few figures of solutions under several different cases are shown when aleatoric constants and variables are given exact values.

Direct perturbation analysis on the localized waves of the modified nonlinear Schrödinger equation under nonvanishing boundary condition

2016 ◽  
Vol 30 (11) ◽  
pp. 1650179
Author(s):  
Min Li ◽  
Tao Xu ◽  
Lei Wang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Pulse Compression ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Perturbation ◽  
Nonlinear Schrödinger ◽  
Direct Perturbation

In this paper, the modified nonlinear Schrödinger equation is investigated via the direct perturbation method, which can describe the femtosecond optical pulse propagation in a monomodal optical fiber. Considering the quintic nonlinear perturbation, we obtain the approximate solution with the first-order correction, which can be expressed by the solution and symmetry of the derivative nonlinear Schrödinger equation. Under the nonvanishing boundary conditions, the approximate dark and anti-dark soliton solutions are derived and the existence conditions are also given. The effects of the perturbation on the propagations and interactions of the solitons on the nonzero background are discussed by comparing the physical quantities of solitons with the unperturbed case. It is found that the quintic nonlinear perturbation can lead to the change of the velocity as well as the pulse compression, but has no influence on the dynamics of the elastic interactions. Finally, numerical simulations are performed to support the theoretical results.

Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 2. Soliton solutions and integrability

1993 ◽  
Vol 50 (3) ◽  
pp. 457-476 ◽  
Author(s):  
Bernard Deconinck ◽  
Peter Meuris ◽  
Frank Verheest
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Mhd Waves ◽  
Displacement Current ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

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