PSEUDORECURRENCE AND CHAOS OF CUBIC-QUINTIC NONLINEAR SCHRÖDINGER EQUATION

1996 ◽  
Vol 07 (06) ◽  
pp. 775-786 ◽  
Author(s):  
CANGTAO ZHOU ◽  
C. H. LAI
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Arbitrary Parameter ◽  
Nonlinear Schrödinger ◽  
Parameter Values ◽  
Theoretical Analyses

Recurrence, pseudorecurrence, and chaotic solutions for a continuum Hamiltonian system in which there exist spatial patterns of solitary wave structures are investigated using the nonlinear Schrödinger equation (NSE) with cubic and quintic terms. The theoretical analyses indicate that there may exist Birkhoff's recurrence for the arbitrary parameter values. The numerical experiments show that there may be Fermi–Pasta–Ulam (FPU) recurrence, pseudorecurrence, and chaos when different initial conditions are chosen. The fact that the system energy is effectively shared by finite Fourier modes suggests that it may be possible to describe the continuum system in terms of some effective degrees of freedom.

scholarly journals ASYMPTOTIC STABILITY OF NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL

2005 ◽  
Vol 17 (10) ◽  
pp. 1143-1207 ◽  
Author(s):  
ZHOU GANG ◽  
I. M. SIGAL
Keyword(s):  
Asymptotic Stability ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Generalized Nonlinear Schrödinger Equation

We prove asymptotic stability of trapped solitons in the generalized nonlinear Schrödinger equation with a potential in dimension 1 and for even potential and even initial conditions.

scholarly journals On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Neveen G. A. Farag ◽  
Ahmed H. Eltanboly ◽  
M. S. EL-Azab ◽  
S. S. A. Obayya
Keyword(s):  
Schrödinger Equation ◽  
Fiber Optics ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Real Life ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Numerical Approaches

In this paper, four compelling numerical approaches, namely, the split-step Fourier transform (SSFT), Fourier pseudospectral method (FPSM), Crank-Nicolson method (CNM), and Hopscotch method (HSM), are exhaustively presented for solving the 1D nonlinear Schrodinger equation (NLSE). The significance of this equation is referred to its notable contribution in modeling wave propagation in a plethora of crucial real-life applications such as the fiber optics field. Although exact solutions can be obtained to solve this equation, these solutions are extremely insufficient because of their limitations to only a unique structure under some limited initial conditions. Therefore, seeking high-performance numerical techniques to manipulate this well-known equation is our fundamental purpose in this study. In this regard, extensive comparisons of the proposed numerical approaches, against the exact solution, are conducted to investigate the benefits of each of them along with their drawbacks, targeting a broad range of temporal and spatial values. Based on the obtained numerical simulations via MATLAB, we extrapolated that the SSFT invariably exhibits the topmost robust potentiality for solving this equation. However, the other suggested schemes are substantiated to be consistently accurate, but they might generate higher errors or even consume more processing time under certain conditions.

scholarly journals Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation

2020 ◽  
Vol 4 (3) ◽  
pp. 41 ◽  
Author(s):  
Hulya Durur ◽  
Esin Ilhan ◽  
Hasan Bulut
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Complex Wave ◽  
Novel Complex ◽  
Parameter Values

This manuscript focuses on the application of the (m+1/G′)-expansion method to the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. With the help of projected method, the periodic and singular complex wave solutions to the considered model are derived. Various figures such as 3D and 2D surfaces with the selecting the suitable of parameter values are plotted.

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