Lumps and rogue waves on the periodic backgrounds for a (2 + 1)-dimensional nonlinear Schrödinger equation in a Heisenberg ferromagnetic spin chain

2021 ◽  
pp. 2150321
Author(s):  
Xia-Xia Du ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Chen-Rong Zhang ◽  
Su-Su Chen
Keyword(s):  
Periodic Solutions ◽  
Spin Chain ◽  
Communication Systems ◽  
Anisotropy Parameter ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Lattice Parameter ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Heisenberg Ferromagnetic Spin Chain

Spin excitations for the magnetic materials are used in the nonlinear signal processing devices and microwave communication systems. Under consideration in this paper is a [Formula: see text]-dimensional nonlinear Schrödinger (NLS) equation which describes the spin dynamics for a Heisenberg ferromagnetic spin chain. Through a reduced transformation, we convert such an equation into the [Formula: see text]-dimensional focusing NLS equation. Via the rogue-periodic solutions associated with two types of the Lie symmetry transformations of the NLS equation, we present the lump- and rogue-periodic solutions. Besides, the lump and mixed lump-soliton solutions are deduced. We graphically investigate the lump- and rogue-periodic waves and find that the amplitudes of the lumps and rogue waves are negatively related to [Formula: see text] and [Formula: see text]; the distances between two valleys of the lumps and widths of the rogue waves are affected by [Formula: see text] and [Formula: see text], where [Formula: see text] is the uniaxial crystal field anisotropy parameter, [Formula: see text] and [Formula: see text] are related to the bilinear exchange interaction, [Formula: see text] is the lattice parameter.

Hybrid soliton solutions in the (2+1)-dimensional nonlinear Schrödinger equation

2017 ◽  
Vol 31 (32) ◽  
pp. 1750298 ◽  
Author(s):  
Meidan Chen ◽  
Biao Li
Keyword(s):  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Nls Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit

Rational solutions and hybrid solutions from N-solitons are obtained by using the bilinear method and a long wave limit method. Line rogue waves and lumps in the (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger (NLS) equation are derived from two-solitons. Then from three-solitons, hybrid solutions between kink soliton with breathers, periodic line waves and lumps are derived. Interestingly, after the collision, the breathers are kept invariant, but the amplitudes of the periodic line waves and lumps change greatly. For the four-solitons, the solutions describe as breathers with breathers, line rogue waves or lumps. After the collision, breathers and lumps are kept invariant, but the line rogue wave has a great change.

SOLITONS AND OTHER SOLUTIONS FOR THE (2+1)-DIMENSIONAL HEISENBERG FERROMAGNETIC SPIN CHAIN EQUATION USING IMPROVED MODIFIED EXTENDED TANH-FUNCTION METHOD

2021 ◽  
Vol 10 (11) ◽  
pp. 3491-3504
Author(s):  
A. Darwish ◽  
H.M. Ahmed ◽  
M. Ammar ◽  
M.H. Ali ◽  
A.H. Arnous
Keyword(s):  
Periodic Solutions ◽  
Exponential Function ◽  
Spin Chain ◽  
Function Method ◽  
Chain Model ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Spin Chain Model ◽  
Chain Equation

This paper studies $(2 + 1)$-dimensional Heisenberg ferromagnetic spin chain model by using improved modified extended tanh-function method. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic solutions, Weierstrass elliptic periodic type solutions and exponential function solutions. Moreover, some of the obtained solutions are represented graphically.

A variable coefficient nonlinear Schrödinger equation: localized waves on the plane wave background and their dynamics

2019 ◽  
Vol 33 (10) ◽  
pp. 1850121 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Variable Coefficient ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Plane Wave Background ◽  
Localized Waves ◽  
Similarity Reductions

In this work, a variable coefficient nonlinear Schrödinger (vc-NLS) equation is under investigation, which can describe the amplification or absorption of pulses propagating in an optical fiber with distributed dispersion and nonlinearity. By means of similarity reductions, a similar transformation helps us to relate certain class of solutions of the standard NLS equation to the solutions of integrable vc-NLS equation. Furthermore, we analytically consider nonautonomous breather wave, rogue wave solutions and their interactions in the vc-NLS equation, which possess complicated wave propagation in time and differ from the usual breather waves and rogue waves. Finally, the main characteristics of the rational solutions are graphically discussed. The parameters in the solutions can be used to control the shape, amplitude and scale of the rogue waves.

Dark solitons, Lax pair and infinitely-many conservation laws for a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in the inhomogeneous Heisenberg ferromagnetic spin chain

2017 ◽  
Vol 31 (03) ◽  
pp. 1750013 ◽  
Author(s):  
Xue-Hui Zhao ◽  
Bo Tian ◽  
De-Yin Liu ◽  
Xiao-Yu Wu ◽  
Jun Chai ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Spin Chain ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Nonlinear Schrodinger Equation ◽  
Dark Solitons ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Dimensional Variable

Under investigation in this paper is a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain. Lax pair and infinitely-many conservation laws are derived, indicating the existence of the multi-soliton solutions for such an equation. Via the Hirota method with an auxiliary function, bilinear forms, dark one-, two- and three-soliton solutions are derived. Propagation and interactions for the dark solitons are illustrated graphically: Velocity of the solitons is linearly related to the coefficients of the second- and fourth-order dispersion terms, while amplitude of the solitons does not depend on them. Interactions between the two solitons are shown to be elastic, while those among the three solitons are pairwise elastic.

Exact Localized and Periodic Solutions of the Ablowitz-Ladik Discrete Nonlinear Schrödinger System

2005 ◽  
Vol 60 (8-9) ◽  
pp. 573-582 ◽  
Author(s):  
Xian-jing Lai ◽  
Jie-fang Zhang
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Pacs 02.30 ◽  
Schrödinger System ◽  
Jacobian Functions

We have studied, analytically, the Ablowitz-Ladik discrete nonlinear Schr¨odinger system. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobian functions, bright and dark soliton solutions, and quasi-periodic solutions. We have also found the range of parameters where each exact solution exists. - PACS: 02.30.Jr, 05.45.Yv, 42.65.Tg, 02.30.Gp.

SYMBOLIC COMPUTATION STUDY OF BRIGHT SOLITONIC PULSES IN THE NORMAL DISPERSION REGION

2008 ◽  
Vol 17 (03) ◽  
pp. 235-242 ◽  
Author(s):  
WEN-JUN LIU ◽  
BO TIAN ◽  
TAO XU
Keyword(s):  
Symbolic Computation ◽  
Optical Communication ◽  
Potential Application ◽  
Communication Systems ◽  
The Novel ◽  
Nls Equation ◽  
Normal Dispersion ◽  
Dispersion Region ◽  
Nonlinear Schrödinger ◽  
Optical Communication Systems

New types of solitonic pulses are obtained theoretically based on the solutions for the nonlinear Schrödinger (NLS) equation. Unlike the earlier results, in the normal dispersion region, the novel bright solitonic pulses are observed. Depending on the parameters' values, the properties of both bright and dark solitonic pulses are described in the same expression. Furthermore, those solitonic pulses are found to be evolved into bright and dark ones under certain conditions. This might be a potential application in optical communication systems which can produce bright and dark solitonic pulses simultaneously.

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