Exact solutions for the quintic nonlinear Schrödinger equation with time and space

Using similarity transformations, the analytical solutions to the quintic nonlinear Schrödinger equation with potentials and nonlinearities depending both on time and space are constructed. The stability of resonance solitons is examined by direct numerical simulation. It is found that stable fundam...

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Bibliographic Details
Published in:Nonlinear dynamics 2016-04, Vol.84 (1), p.251-259
Main Authors: Xu, Si-Liu, Petrović, Nikola, Belić, Milivoj R., Deng, Wenwu
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Computer simulation
Control
Defocusing
Direct numerical simulation
Dynamical Systems
Engineering
Exact solutions
Mathematical analysis
Mechanical Engineering
Nonlinearity
Original Paper
Schrodinger equation
Schroedinger equation
Similarity
Solitary waves
Solitons
Transformations
Vibration
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Summary:Using similarity transformations, the analytical solutions to the quintic nonlinear Schrödinger equation with potentials and nonlinearities depending both on time and space are constructed. The stability of resonance solitons is examined by direct numerical simulation. It is found that stable fundamental soliton states with m = 0 and low-order soliton states with m = 1 can be supported both by self-focusing and self-defocusing materials. Higher-order solitons are found unstable, however, displaying quasi-stable propagation over prolonged distances.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-015-2426-1