# Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations

Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations A study of high-order solitons in three nonlocal nonlinear Schrödinger equations is presented. These include the $$\mathcal {PT}$$ PT -symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schrödinger equations. General high-order solitons in three different equations are derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except for the difference in the corresponding symmetry relations on the “perturbed” scattering data. Dynamics of general high-order solitons in these equations is further analyzed. It is shown that the high-order fundamental-soliton is moving on several different trajectories in nearly equal velocities, and they can be nonsingular or repeatedly collapsing, depending on the choices of the parameters. It is also shown that the high-order multi-solitons could have more complicated wave structures and behave very differently from high-order fundamental-solitons. More interestingly, via the combinations of different size of block matrix in the Riemann–Hilbert solutions, high-order hybrid-pattern solitons are found, which describe the nonlinear interaction between several types of solitons. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

# Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations

Nonlinear Dynamics, Volume 94 (1) – May 29, 2018
14 pages

/lp/springer_journal/dynamics-of-high-order-solitons-in-the-nonlocal-nonlinear-schr-dinger-d2uYMXlZWz
Publisher
Springer Journals
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
DOI
10.1007/s11071-018-4373-0
Publisher site
See Article on Publisher Site

### Abstract

A study of high-order solitons in three nonlocal nonlinear Schrödinger equations is presented. These include the $$\mathcal {PT}$$ PT -symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schrödinger equations. General high-order solitons in three different equations are derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except for the difference in the corresponding symmetry relations on the “perturbed” scattering data. Dynamics of general high-order solitons in these equations is further analyzed. It is shown that the high-order fundamental-soliton is moving on several different trajectories in nearly equal velocities, and they can be nonsingular or repeatedly collapsing, depending on the choices of the parameters. It is also shown that the high-order multi-solitons could have more complicated wave structures and behave very differently from high-order fundamental-solitons. More interestingly, via the combinations of different size of block matrix in the Riemann–Hilbert solutions, high-order hybrid-pattern solitons are found, which describe the nonlinear interaction between several types of solitons.

### Journal

Nonlinear DynamicsSpringer Journals

Published: May 29, 2018

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