Example 2: We now study the cubic nonlinear Schrodinger Equation
Laurent, "Global controllability and stabilization for the nonlinear Schrodinger equation
on some compact manifolds of dimension 3," SIAM Journal on Mathematical Analysis, vol.
Ezzeddine, "Finite dimensional global attractor for a semi-discrete nonlinear Schrodinger equation
with a point defect," Applied Mathematics and Computation, vol.
Unlike the KdV-type equation, the nonlinear Schrodinger equations
were used to study the evolution of envelope classical Rossby solitary waves.
Luan, "Multiple solutions for a class of nonlinear Schrodinger equations
," Journal of Differential Equations, vol.
We consider the following system of nonlinear Schrodinger equations
In Section 2, the exact matter-wave soliton solutions of the variable coefficient cubic-quintic nonlinear Schrodinger equation
are obtained by using similarity transformation.
The work about the behavior of solutions of the nonlinear Schrodinger equation
in the semiclassical limit (s*0) was entirely motivated by a natural mathematicalquestion , however, in the recent years many researches show that the semiclassical limit of Schrodinger equation is also of direct importance to basic physics and technology in nonlinear optics [5-7].
Fifteen papers from two March 2011 conferences explore harmonic analysis techniques for studying higher order elliptic systems with irregular coefficients, the behavior of solutions to the focusing quintic nonlinear Schrodinger equation
, nonlinear wave equations with null structures, and the transverse stability of periodic traveling waves.
Therefore, once the real motions of the microscopic particles and background fields and their true interactions are considered, then the properties and states of microscopic particles cannot be described by Schrodinger Equation (1), but should be depicted by the following nonlinear Schrodinger equation
in nonlinear quantum systems
The method of calculation implemented in this software is based on solving the nonlinear Schrodinger equation
. The non-linear Schrodinger equation is the partial differential equation and is a classical optical wave propagation approximation in the optical fiber .
Farahrooz: Exact solutions of the nonlinear Schrodinger equation
by the first integral method,J.Math.