scholarly journals Existence of Dark Soliton Solutions of the Cubic Nonlinear Schrödinger Equation with Periodic Inhomogeneous Nonlinearity

2008 ◽  
Vol 15 (sup3) ◽  
pp. 65-72 ◽  
Author(s):  
Juan Belmonte-Beitia ◽  
Pedro J Torres
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Cubic Nonlinear Schrödinger Equation

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.

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.

scholarly journals New Optical Soliton Solutions For The Variable Coefficients Nonlinear Schrodinger Equation

2021 ◽  
Author(s):  
Yongyi Gu ◽  
Najva Aminakbari
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Optical Soliton ◽  
Nonlinear Schrödinger

Abstract This paper is appropriated to seek new optical soliton solutions of nonlinear Schrodinger equation (NLSE) with time-dependent coefficients which describes the dispersion decreasing fiber. By proposing Bernoulli (G ′/G)-expansion method, where G = G(ζ ) satisfies Bernoulli equation, some periodic wave, bright and dark soliton solutions are successfully achieved. In addition, 3D, line and contour maps graphs of the obtained results under effect of different values of coefficients are illustrated to have acceptable conception of dynamic structures.

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