A study of periodic solutions and periodic background solutions for the reverse-space–time modified nonlinear Schrödinger equation

Ye, Hui; Guo, Rui

doi:10.1016/j.wavemoti.2022.103112

Cited by 3 publications

(4 citation statements)

References 31 publications

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“…The forms of the breathers on the singleperiodic background and the rogue waves on the single-periodic background are the same as [37,48]. The forms of the hybrid rogue waves and breather solutions on the singleperiodic background are the same as [40,41] From (12), when n = 2, k = 1, l = 0, we define λ 1 = β 1 , λ 2 = β 2 and β 2 ≠ ± β 1 . A double-periodic wave solution can be obtained.…”

Section: Hybrid Rogue Waves and Breathers Solutions On The Singleperi...mentioning

confidence: 99%

“…DT and semi-degenerate DTs are used to construct the hybrid breather-rogue waves of the reverse-space-time modified NLS equation on the doubleperiodic background [41]. By comparison, we find that the properties of the solutions on the double-periodic background are more complex than those on the single-periodic background [41]. It is necessary to study the hybrid solutions on the double-periodic background.…”

Section: Introductionmentioning

confidence: 99%

“…On the basis of these solutions [34][35][36][37][38][39], some hybrid solutions of nonlinear waves on the periodic background have been constructed, DT and semidegenerate DT are used to construct the hybrid breather-rogue wave of derivative nonlinear Schrödinger equation (DNLS) on the periodic background [40]. DT and semi-degenerate DTs are used to construct the hybrid breather-rogue waves of the reverse-space-time modified NLS equation on the doubleperiodic background [41]. By comparison, we find that the properties of the solutions on the double-periodic background are more complex than those on the single-periodic background [41].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Jiang,

Zhaqilao

2024

Commun. Theor. Phys.

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In this paper, by using Darboux transformation (DT) method and Taylor expansion method, a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of Kundu-DNLS equation is constructed when n is even. Breathers and rogue waves can be obtained from this determinant, respectively. Further, the hybrid rogue waves and breathers solutions on the different periodic background are given explicitly, including the single-periodic background, the double-periodic background and the plane wave background by selecting different parameters. In addition, the form of the obtained solutions is summarized.

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Section: Hybrid Rogue Waves and Breathers Solutions On The Singleperi...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Jiang,

Zhaqilao

2024

Commun. Theor. Phys.

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“…Among these methods, the DT is widely recognized as a powerful tool to obtain the exact solutions for the integrable systems. Currently, the DT has been applied to obtain the exact solutions for the integrable systems on the plane wave, trigonometric function, Jacobian elliptic function and multi-periodic backgrounds [22,[39][40][41][42]. To the best of our knowledge, the multi-soliton solutions and breathers of equation ( 4) have not been studied by the iterative N-fold DT.…”

Section: Introductionmentioning

confidence: 99%

Magnetic soliton and breather interactions for the higher-order Heisenberg ferromagnetic equation via the iterative N-fold Darboux transformation

Liu,

Wen,

Zhang

2024

Phys. Scr.

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This paper focuses on a higher-order Heisenberg ferromagnetic equation, which may describe the motion of the magnetic vector of isotropic ferromagnetism. The iterative N-fold Darboux transformation is ﬁrst constructed to generate the dark and anti-dark magnetic solitons on the non-zero constant backgrounds, bright and dark breathers on the trigonometric function and non-zero constant backgrounds as well as breathers on the trigonometric function and vanishing backgrounds. We discover that the soliton structures of three diﬀerent components can generate rotation with diﬀerent constant seed solutions. Meanwhile, the trajectory curve and the direction of the magnetic vector are also discussed from the perspective of magnetism, we ﬁnd that for constant seed solutions, the motion of the magnetic vector is limited to the hemisphere, while for trigonometric seed solutions, the motion of the magnetic vector can be distributed throughout the whole sphere. These novel phenomena may be helpful to understand the dynamics of the magnetic vector in the magnetic materials.

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The nonlocal coupled nonlinear Schrödinger system with 𝒫𝒯-symmetric: Analytical solutions under two types of Darboux transformation

Niu

Guo

2023

Mod. Phys. Lett. B

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The coupled nonlinear Schrödinger (CNLS) system is often used to describe physical problems such as wave propagation in a birefringent optical fiber. Under investigation in this paper is the nonlocal [Formula: see text]-symmetric reverse-space type of CNLS system, through constructing two types of Darboux transformation (DT), we will derive a new series of nonlocal analytic solutions: (1) Single-periodic and double-periodic solutions; (2) Four different combinations about dark and anti-dark solitons, as well as the bright and dark breathers on a periodic background. Moreover, the fundamental properties and dynamical behaviors of those solutions will be discussed.

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A study of periodic solutions and periodic background solutions for the reverse-space–time modified nonlinear Schrödinger equation

Cited by 3 publications

References 31 publications

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Magnetic soliton and breather interactions for the higher-order Heisenberg ferromagnetic equation via the iterative N-fold Darboux transformation

The nonlocal coupled nonlinear Schrödinger system with 𝒫𝒯-symmetric: Analytical solutions under two types of Darboux transformation

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