scholarly journals Soliton in an extended nonlinear Schrödinger equation with stimulated scattering on damping low-frequency waves and nonlinear dispersion

2015 ◽  
Vol 574 ◽  
pp. 012032
Author(s):  
E M Gromov
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Low Frequency ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Dispersion ◽  
Stimulated Scattering ◽  
Nonlinear Schrödinger ◽  
Low Frequency Waves

ON NEW EXACT SPECIAL SOLUTIONS OF THEGNLS(m,n,p,q) EQUATIONS

2010 ◽  
Vol 24 (16) ◽  
pp. 1769-1783 ◽  
Author(s):  
MUSTAFA INÇ
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Dispersion ◽  
Nonlinear Schrödinger ◽  
Special Solutions ◽  
Generalized Nonlinear Schrödinger Equation

In this paper, we establish exact special solutions of the generalized nonlinear Schrödinger equation with nonlinear dispersion (called the GNLS (m,n,p,q) equation) by using a sn - cn method. Some new Jacobi elliptic, envelope compacton and solitary pattern solutions of GNLS (m,n,p,q) equations are obtained.

Nonlinear dispersion relation for nonlinear Schrödinger equation

1988 ◽  
Vol 39 (2) ◽  
pp. 297-302 ◽  
Author(s):  
J. C. Bhakta
Keyword(s):  
Dispersion Relation ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Instability Region ◽  
Nonlinear Dispersion ◽  
Nonlinear Schrödinger ◽  
Nonlinear Dispersion Relation ◽  
Cubic Nonlinear Schrödinger Equation

By using the average-Lagrangian method (average variational principle), a nonlinear dispersion relation has been derived for the cubic nonlinear Schrödinger equation. It is found that the size of the instability region in wavenumber space decreases with increasing field amplitude in comparison with the linear theory.

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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