Soliton solutions for Hirota–Maxwell–Bloch system and its nonlocal form

2021 ◽  
Author(s):  
Jia-Huan Guo ◽  
Rui Guo
Keyword(s):  
Rogue Wave ◽  
Modulation Frequency ◽  
Soliton Solutions ◽  
Pt Symmetry ◽  
Darboux Transformations ◽  
Continuous Waves ◽  
Generative Mechanism

This paper studies the Hirota–Maxwell–Bloch (H–MB) system and its nonlocal form. Based on the Darboux Transformations (DTs), for H–MB system, we present general double breathers, what is more, we take appropriate modulation frequency and position parameters to investigate the generative mechanism of rogue wave sequences and different periodic breather sequences. For nonlocal Hirota–Maxwell–Bloch (NH–MB) system, we discuss symmetry preserving and broken soliton solutions under zero background. Besides, we present nine combinations of dark and antidark soliton solutions under continuous waves background when PT-symmetry is broken.

Multiple rogue and soliton wave solutions to the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation arising in fluid mechanics and plasma physics

2021 ◽  
pp. 2150383
Author(s):  
Onur Alp Ilhan ◽  
Sadiq Taha Abdulazeez ◽  
Jalil Manafian ◽  
Hooshmand Azizi ◽  
Subhiya M. Zeynalli
Keyword(s):  
Rogue Wave ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Novel ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Soliton Wave Solutions

Under investigation in this paper is the generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt equation. Based on bilinear method, the multiple rogue wave (RW) solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions for the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue wave solutions are obtained via Maple 18 software. The exact lump and RW solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters, will be constructed. Via various three-dimensional plots and density plots, dynamical characteristics of these waves are exhibited.

A coupled nonlinear Schrödinger-type equation and its Darboux transformation

2018 ◽  
Vol 32 (17) ◽  
pp. 1850192 ◽  
Author(s):  
Xianguo Geng ◽  
Jiao Wei ◽  
Bo Xue
Keyword(s):  
Spectral Problem ◽  
Trivial Solution ◽  
Power Flow ◽  
Soliton Solutions ◽  
Type Equation ◽  
Reduction Technique ◽  
Explicit Solutions ◽  
Darboux Transformations ◽  
Negative Power ◽  
Nonlinear Schrödinger

A new coupled nonlinear Schrödinger (NLS)-type equation is proposed by means of the negative power flow of a spectral problem. Resorting to the gauge transformation of the spectral problem and the reduction technique, Darboux transformations for the coupled NLS-type equation and its reduction are constructed, by which explicit solutions of the two coupled NLS-type equations can be engendered from their known solutions. This process can be done continually and will usually yield a series of solutions including multi-soliton solutions. As an illustrate example, one- and two-soliton solutions of the latter coupled NLS-type equation are obtained from a trivial solution.

Noncommutative coupled complex modified Korteweg–de Vries equation: Darboux and binary Darboux transformations

2019 ◽  
Vol 34 (07n08) ◽  
pp. 1950054
Author(s):  
H. Wajahat A. Riaz
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Evolution Equations ◽  
Order Effects ◽  
Darboux Transformations ◽  
De Vries ◽  
Higher Order Effects

Higher-order nonlinear evolution equations are important for describing the wave propagation of second- and higher-order number of fields in optical fiber systems with higher-order effects. One of these equations is the coupled complex modified Korteweg–de Vries (ccmKdV) equation. In this paper, we study noncommutative (nc) generalization of ccmKdV equation. We present Darboux and binary Darboux transformations (DTs) for the nc-ccmKdV equation and then construct its Quasi-Grammian solutions. Further, single and double-hump soliton solutions of first- and second-order are given in commutative settings.

TWO ENLARGED LOOP ALGEBRAS FOR OBTAINING NEW INTEGRABLE HIERARCHIES

2011 ◽  
Vol 25 (19) ◽  
pp. 2637-2656
Author(s):  
YUFENG ZHANG ◽  
HONWAH TAM ◽  
WEI JIANG
Keyword(s):  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Soliton Solutions ◽  
Loop Algebra ◽  
Darboux Transformations ◽  
Soliton Equation ◽  
Hamiltonian Structures ◽  
Soliton Theory ◽  
Loop Algebras ◽  
Soliton Hierarchy

Taking a loop algebra [Formula: see text] we obtain an integrable soliton hierarchy which is similar to the well-known Kaup–Newell (KN) hierarchy, but it is not. We call it a modified KN (mKN) hierarchy. Then two new enlarged loop algebras of the loop algebra [Formula: see text] are established, respectively, which are used to establish isospectral problems. Thus, two various types of integrable soliton-equation hierarchies along with multi-component potential functions are obtained. Their Hamiltonian structures are also obtained by the variational identity. The second hierarchy is integrable couplings of the mKN hierarchy. This paper provides a clue for generating loop algebras, specially, gives an approach for producing new integrable systems. If we obtain a new soliton hierarchy, we could deduce its symmetries, conserved laws, Darboux transformations, soliton solutions and so on. Hence, the way presented in the paper is an important aspect to obtain new integrable systems in soliton theory.

scholarly journals Solitons, Rogues and Interaction Behaviors of Third-Order Nonlinear Schrodinger Equation

2022 ◽  
Author(s):  
Ren Bo ◽  
Shi Kai-Zhong ◽  
Shou-Feng Shen ◽  
Wang Guo-Fang ◽  
Peng Jun-Da ◽  
...  
Keyword(s):  
Bilinear Form ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Ultrashort Pulses ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Femtosecond Regime ◽  
Wave Limit

Abstract In this paper, we investigate the third-order nonlinear Schr\"{o}dinger equation which is used to describe the propagation of ultrashort pulses in the subpicosecond or femtosecond regime. Based on the independent transformation, the bilinear form of the third-order NLSE is constructed. The multiple soliton solutions are constructed by solving the bilinear form. The multi-order rogue waves and interaction between one-soliton and first-order rogue wave are obtained by the long wave limit in multi-solitons. The dynamics of the first-order rogue wave, second-order rogue wave and interaction between one-soliton and first-order rogue wave are presented by selecting the appropriate parameters. In particular parameters, the positions and the maximum of amplitude of rogue wave can be confirmed by the detail calculations.PACS numbers: 02.30.Ik, 05.45.Yv.

scholarly journals Multi-rogue Wave Solutions for a Generalized Integrable Discrete Nonlinear Schrodinger Equation With Higher-order Excitations

2021 ◽  
Author(s):  
Ma Li-Yuan ◽  
Yang Jun ◽  
Zhang Yan-Li
Keyword(s):  
Modulation Instability ◽  
Rogue Wave ◽  
Order Term ◽  
Higher Order ◽  
Discrete Version ◽  
Nls Equation ◽  
Third Order ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Dynamical Behaviors ◽  
Continuous Waves

Abstract In this paper, we construct the discrete rogue wave(RW) solutions for a higher-order or generalized integrable discrete nonlinear Schr¨odinger(NLS) equation. First, based on the modified Lax pair, the discrete version of generalized Darboux transformation are constructed. Second, the dynamical behaviors of first-, second- and third-order RWsolutions are investigated in corresponding to the unique spectral parameter λ, higher-order term coefficient γ, and free constants dk, fk (k = 1, 2, · · · ,N), which exhibit affluent wave structures. The differences between the RW solution of the higher-order discrete NLS equation and that of the Ablowitz-Ladik(AL) equation are illustrated in figures. Moreover, numerical experiments are explored, which demonstrates that strong-interaction RWs are stabler than the weak-interaction RWs. Finally, the modulation instability of continuous waves is studied.

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