# Discrete bright–dark soliton solutions and parameters controlling for the coupled Ablowitz–Ladik equation

Discrete bright–dark soliton solutions and parameters controlling for the coupled... We consider the nonautonomous discrete vector bright–dark solutions and their controllable behaviors in the coupled Ablowitz–Ladik equation with variable coefficients, which possesses complicated wave propagation in time. Based on the differential–difference symmetry transformation and the Lamé polynomial solutions, we use the Jacobi elliptic functions $$\hbox {sn}(n, m), \hbox {cn}(n, m)$$ sn ( n , m ) , cn ( n , m ) , $$\hbox {dn}(n, m)$$ dn ( n , m ) and present the nonautonomous discrete vector bright–dark solutions, which are localized in space and keep the localization longer in time. Moreover, we also exhibit the wave propagation of nonautonomous Lamé polynomial solutions of higher order and their dynamics for some chosen parameters and functions. And the managements and dynamic behaviors of these solutions are investigated analytically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

# Discrete bright–dark soliton solutions and parameters controlling for the coupled Ablowitz–Ladik equation

, Volume 89 (4) – Jun 6, 2017
12 pages

/lp/springer_journal/discrete-bright-dark-soliton-solutions-and-parameters-controlling-for-XzwO5hnNYF
Publisher
Springer Netherlands
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3593-z
Publisher site
See Article on Publisher Site

### Abstract

We consider the nonautonomous discrete vector bright–dark solutions and their controllable behaviors in the coupled Ablowitz–Ladik equation with variable coefficients, which possesses complicated wave propagation in time. Based on the differential–difference symmetry transformation and the Lamé polynomial solutions, we use the Jacobi elliptic functions $$\hbox {sn}(n, m), \hbox {cn}(n, m)$$ sn ( n , m ) , cn ( n , m ) , $$\hbox {dn}(n, m)$$ dn ( n , m ) and present the nonautonomous discrete vector bright–dark solutions, which are localized in space and keep the localization longer in time. Moreover, we also exhibit the wave propagation of nonautonomous Lamé polynomial solutions of higher order and their dynamics for some chosen parameters and functions. And the managements and dynamic behaviors of these solutions are investigated analytically.

### Journal

Nonlinear DynamicsSpringer Journals

Published: Jun 6, 2017

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