Kink Waves in an Extended Nonlinear Schrödinger Equation with Allowance for Stimulated Scattering and Nonlinear Dispersion

2014 ◽  
Vol 57 (4) ◽  
pp. 279-286 ◽  
Author(s):  
E. M. Gromov ◽  
V. V. Tyutin
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Dispersion ◽  
Stimulated Scattering ◽  
Nonlinear Schrödinger ◽  
Kink 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.

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