scholarly journals Soliton dynamics for the nonlinear Schrödinger equation with magnetic field

2009 ◽  
Vol 130 (4) ◽  
pp. 461-494 ◽  
Author(s):  
Marco Squassina
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Soliton Dynamics

Integrability and soliton dynamics for an inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma

2015 ◽  
Vol 29 (26) ◽  
pp. 1550152 ◽  
Author(s):  
Yu-Feng Wang ◽  
Bo Tian
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Inhomogeneous Plasma ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Bell Polynomial ◽  
Nonlinear Schrödinger ◽  
Soliton Dynamics ◽  
Inhomogeneous Nonlinear Schrödinger Equation

Under investigation in this paper is an inhomogeneous nonlinear Schrödinger equation, which describes the propagation of a large-wavelength small-amplitude electron plasma wave in a parabolic-distributed and constant-interactional-damping inhomogeneous plasma. Via the Hirota method, Bell-polynomial approach and symbolic computation, bilinear form, Bäcklund transformation and [Formula: see text]-soliton solutions are obtained. Influence of the linear density coefficient [Formula: see text] and damping coefficient [Formula: see text] on the soliton envelopes is also discussed, i.e. [Formula: see text] can affect the soliton position, while [Formula: see text] is related to the soliton intensity, velocity and phase shift. Periodically attractive and repulsive interactions are shown. Asymptotic analysis shows that the interactions between/among the solitons are elastic.

scholarly journals Soliton dynamics in an extended nonlinear Schrödinger equation with a spatial counterpart of the stimulated Raman scattering

2013 ◽  
Vol 79 (6) ◽  
pp. 1057-1062 ◽  
Author(s):  
E. M. GROMOV ◽  
B. A. MALOMED
Keyword(s):  
Schrödinger Equation ◽  
Raman Scattering ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stimulated Raman Scattering ◽  
Low Frequency ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Soliton Dynamics ◽  
Stimulated Raman

AbstractThe dynamics of solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high-frequency (HF) and low-frequency (LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves in plasmas. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (PSRS) term, i.e. a spatial-domain counterpart of the SRS term, which is well known as an ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order diffraction (SOD). It is shown that the wavenumber downshift of solitons, caused by the PSRS, may be compensated by an upshift provided by the SOD whose coefficient is a linear function of the coordinate. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well, including the predicted balance between the PSRS and the linearly inhomogeneous SOD.

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