推广的导数非线性薛定谔方程的单/双周期背景上的呼吸子和怪波及其碰撞解

Abstract

Abstract:

The nonlinear Schr $\rm\ddot{o}$ dinger equation is a very important integrable system in the field of physics and applied mathematics. In this paper, the breather and rogue wave on the periodic/double periodic background and the collision solutions of breather and rogue wave for the generalized derivative nonlinear Schr $\rm\ddot{o}$ dinger equation are studied by using the Darboux transformation. Firstly, the Darboux transformation of the generalized derivative nonlinear Schr $\rm\ddot{o}$ dinger equation is constructed. Then, by using the Darboux transformation, the breather and rogue wave on the periodic/double periodic background and the collision solutions are derived. Finally, by means of the figures, the structures of interesting new solutions are analyzed in detail, which also provide a theoretical basis for studying the physical mechanism of the new solution.

Key words: The generalized derivative nonlinear Schr?dinger equation, Darboux transformation, Periodic solution, Breather, Rogue wave

CLC Number:

0175.24

Lou Yu, Zhang Yi. Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schr $\rm\ddot{o}$ dinger Equation[J].Acta mathematica scientia,Series A, 2024, 44(6): 1511-1519.

Trendmd

Figures/Tables 7

References 29

[1]	Olver P J, Sattinger D H. Solitons in Physics, Mathematics, and Nonlinear Optics. New York: Springer, 1990
[2]	Burger S, Bongs K, Dettmer S, Ertmer W, Sengstock K. Dark solitons in Bose-Einstein condenstates. Phys Rev Lett, 1999, 83: 5198-5201
[3]	Bludov Y V, Konotop V V, Akhmediev N. Matter rogue waves. Phys Rev A, 2009, 80: 033610
[4]	Yang B, Chen Y. Dynamics of high-order solitons in the nonlocal nonlinear Schr $\rm\ddot{o}$ dinger equations. Nonlinear Dynam, 2018, 94: 489-502
[5]	Ma W X. Riemann-Hilbert problems of a six-component mKdV system and its soliton solutions. Acta Math Sci, 2019, 29(2): 509-523
[6]	Akhmediev N, Korbeev V I. Modulation instability and periodic soulutions of the nonlinear Schr $\rm\ddot{o}$ dinger equation. Theoret Math Phys, 1986, 69: 1089-1093
[7]	Kuznetsov E A. Solitons in a parametrically unstable plasma. Dokl Akad Nauk SSSR, 1977, 236: 575-577
[8]	Priya N V, Senthilvelan M, Lakshmanan M. Akhmediev breathers, Ma solitons and general breathers from rogue waves: A case study in the Manakov system. Phys Rev E, 2013, 88(2): 022918
[9]	Akhmediev N, Ankiewicz A, Taki M. Waves that appear from nowhere and disappear without a trace. Phys Lett A, 2009, 373: 675-678
[10]	Wu X H, Gao Y T, Yu X, et al. Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmana-Porsezian-Daniel equation. Wave Motion, 2022, 114: 103036
[11]	Zhai Y Y, Ji T, Geng X G. Coupled derivative nonlinear Schr $\rm\ddot{o}$ dinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber. Appl Math Comput, 2021, 411: 126551
[12]	L $\rm\ddot{u}$ Xing, Chen S J. Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types. Nonlinear Dynam, 2021, 103: 947-977
[13]	房春梅, 田守富. 约化的(3+1)维 Hirota 方程的呼吸波解、Lump 解和半有理解. 数学物理学报, 2022, 42A(3): 775-783
	Fang C M, Tian S F. Breather Wave Solutions, Lump solutions and semi-rational solutions of a reduced (3+1) dimensional Hirota equation. Acta Math Sci, 2022, 42A(3): 775-783
[14]	Ma W X. Bilinear equations and resonant solutions characterized by Bell polynomials. Rep Math Phys, 2013, 72(1): 41-56
[15]	Ma W X. Trilinear equations, Bell polynomials, and resonant solutions. Front Math China, 2013, 8: 1139-1156
[16]	田守富. 一个广义导数非线性 Schr $\rm\ddot{o}$ dinger 方程的 Riemann-Hilbert 问题: 长时间渐近行为. 中国科学: 数学, 2022, 52(5): 505-542
	Tian S F. Riemann-Hilbert problem to a generalized derivative nonlinear Schr $\rm\ddot{o}$ dinger equation: Long-time asymptotic behavior. Sci Sin Math, 2022, 52(5): 505-542
[17]	Wei H Y, Fan E G, Guo H D. Riemann-Hilbert approach and nonlinear dynamics of the coupled higher-order nonlinear Schr $\rm\ddot{o}$ dinger equation in the birefringent or two-mode fiber. Nonlinear Dynam, 2021, 104: 649-660
[18]	Chen X T, Zhang Y, Ye R S. Riemann-Hilbert approach of the coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization. Appl Anal, 2019, 100(10): 2200-2209
[19]	Hu B B, Xia T C, Ma W X. Riemann-Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg-de Vries equation on the half-line. Appl Math Comput, 2018, 332: 148-159
[20]	Guo B L, Ling L M, Liu Q P, Wu C F. Nonlinear Schr $\rm\ddot{o}$ dinger equation: generalized Darboux transformation and rogue wave solutions. Phys Rev E, 2012, 85: 026607
[21]	Wang X, Wei J. Three types of Darboux transformation and general soliton soulutions for the space-shifted nonlocal PT symmetric nonlinear Schr $\rm\ddot{o}$ dinger equation. Appl Math Lett, 2022, 130: 107998
[22]	Zhang Y, Ye R S, Ma W X. Binary Darboux transformation and soliton solutions for the coupled complex modified Korteweg-de Vries equations. Math Meth Appl Sci, 2019, 43: 613-627
[23]	Fan E G. Integrable evolution systems based on Gerdjikov-Ivanovequations, bi-Hamiltonian structure, finite-dimensional integrable systems and $N$ -fold Darboux transforamtion. J Math Phys, 2000, 41: 7769-7782
[24]	Shen Y, Tian B, Zhou T Y, Gao X T. $N$ -fold Darboux transformation and solitonic interactions for the Kraenkel-Manna-Merle system in a saturated ferromagnetic material. Nonlinear Dynam, 2023, 111: 2641-2649
[25]	Kodama Y J. Optical solitons in a monomode fiber. J Stat Phys, 1985, 39: 597
[26]	Chen J B, Pelinovsky D E, Upsal J. Modulation instability of periodic standing waves in the derivative NLS equation. J Nonlinear Sci, 2021, 31: 58
[27]	Zhang N, Xia T C, Fan E G. A Riemann-Hilbert approach to the Chen-Lee-Liu equation on the half line. Acta Math Appl Sin-E, 2018, 34: 493-515 doi: 10.1007/s10255-018-0765-7
[28]	Xu S W, He J S. The rogue wave and breather solution of the Gerdjikov-Ivanov equation. J Math Phys, 2012, 53: 063507
[29]	Li X Y, Han G F, Zhao Q L. Interactions of localized wave and dynamics analysis in generalized derivative nonlinear Schr $\rm\ddot{o}$ dinger equation. Commun Nonlinear Sci, 2022, 114: 106612

Related Articles 15

[1]	Qian Yuting, Zhou Xueliang, Cheng Zhibo. Existence of Periodic Solutions for $\phi$ -Laplacian Rayleigh Equations with a Singularity [J]. Acta mathematica scientia,Series A, 2024, 44(5): 1183-1193.
[2]	Qian Yuting, Zhou Xueliang, Cheng Zhibo. Existence of Periodic Solutions for $\phi$ -Laplacian Rayleigh Equations with a Singularity [J]. Acta mathematica scientia,Series A, 2024, 44(4): 896-906.
[3]	Yin Ruixia, Wang Zedong, Zhang Long. A Periodic Stage Structure Single-Population Model with Infinite Delay and Feedback Control [J]. Acta mathematica scientia,Series A, 2024, 44(4): 994-1011.
[4]	Yang Jiaopeng, Liang Yong. Solitary and Periodic Solutions of the Generalized b-equation [J]. Acta mathematica scientia,Series A, 2024, 44(3): 670-686.
[5]	Wang Zihuan,Wang Chao. Symmetric and Periodic Solutions for a Class of Weakly Coupled Systems Composed of Two Particles with Obstacles [J]. Acta mathematica scientia,Series A, 2023, 43(5): 1427-1439.
[6]	Shan Yuan. Relative Morse Index and Multiple Solutions for Asymptotically Linear Dirac Equation [J]. Acta mathematica scientia,Series A, 2023, 43(1): 69-81.
[7]	Tang Yuxuan, Zhou Guoquan. The Rogue Wave Solution of MNLS Equation Based on Hirota's Bi-linear Derivative Transformation [J]. Acta mathematica scientia,Series A, 2023, 43(1): 132-142.
[8]	Song Huijuan, Huang Qian, Wang Zejia. Asymptotic Analysis of a Tumor Model with Angiogenesis and a Periodic Supply of External Nutrients [J]. Acta mathematica scientia,Series A, 2023, 43(1): 261-273.
[9]	Jiayu Liu,Hanyu Wei,Yan Zhang,Tiecheng Xia,Hui Wang. Soliton Solutions and Its Nonlinear Dynamics Behavior Research of the Three-Component Four-Order Nonlinear Schrödinger System in Alpha Helical Protein [J]. Acta mathematica scientia,Series A, 2022, 42(6): 1873-1885.
[10]	Xuelei Wang. Large Multiple Periodic Solutions for the 1-Dimensional Sub-Linear p-Laplacian Equation [J]. Acta mathematica scientia,Series A, 2022, 42(5): 1462-1472.
[11]	Nan Deng,Meiqiang Feng. Positive Doubly Periodic Solutions To Telegraph Equations: Existence, Uniqueness, Multiplicity and Asymptotic Behavior [J]. Acta mathematica scientia,Series A, 2022, 42(5): 1360-1380.
[12]	Chunmei Fang,Shoufu Tian. Breather Wave Solutions, Lump Solutions and Semi-Rational Solutions of a Reduced (3+1)Dimensional Hirota Equation [J]. Acta mathematica scientia,Series A, 2022, 42(3): 775-783.
[13]	Shaowen Yao,Wenjie Li,Zhibo Cheng. Nondegeneracy and Uniqueness of Periodic Solution for Third-Order Nonlinear Differential Equations [J]. Acta mathematica scientia,Series A, 2022, 42(2): 454-462.
[14]	Jun Lan. Existence and Multiplicity of Anti-Periodic Solutions for a Class of Second Order Duffing Equation [J]. Acta mathematica scientia,Series A, 2022, 42(2): 463-469.
[15]	Chenyang Xia,Zhenhui Wang,Zhibo Cheng. Positive Periodic Solutions for a Damped Duffing Equation with Singularity of Attractive Type [J]. Acta mathematica scientia,Series A, 2022, 42(1): 131-138.

Metrics

Viewed

Full text

166

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	0	0	0	166

	From	local

	Times	166
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	54

From	Others	local

Times	50	4
Rate	93%	7%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

Comments

Recommended 10

[1]	. Existence of Some Special Conformally-K\"ahler metrics on Certain CP1 Bundles[J]. Acta mathematica scientia,Series A, 0, (): 0 .
[2]	Wei-Min WANG Wei Yan. The convergence problem and dispersive blow-up of the modified Kawahara equation[J]. Acta mathematica scientia,Series A, , (): 0 .
[3]	Xiao Jianrong. Robust Accessible Hyperbolic Repelling Sets[J]. Acta mathematica scientia,Series A, 2024, 44(1): 1 -11 .
[4]	Zhang Tianwei, Li Yongkun. Almost Automorphic Dynamics of Nonlocal Laplacian Saturating Schrödinger-Klein-Gordon Equations[J]. Acta mathematica scientia,Series A, 2024, 44(2): 326 -353 .
[5]	Chen Mingchao, Xue Yanfang. Multiple Solutions for a Class of Quasilinear Schrödinger Equations with a Perturbed Term[J]. Acta mathematica scientia,Series A, 2024, 44(2): 417 -428 .
[6]	Wei Huaquan, Wu Hui, Liu Xiaoji, Jin Hongwei. Properties and Computations of the $\mathfrak{m}$ -WG Inverse[J]. Acta mathematica scientia,Series A, 2024, 44(3): 547 -562 .
[7]	Jin Zhenfeng, Sun Hongrui, Zhang Weimin. Multiplicity and Asymptotic Behavior of Normalized Solutions for Kirchhoff-Type Equation[J]. Acta mathematica scientia,Series A, 2024, 44(4): 871 -884 .
[8]	Xiao Suping, Zhao Yuanzhang. Existence and Nonexistence of Solutions for Nonhomogeneous Dirichlet Exterior Problem to a Semilinear Hyperbolic Differential Inequality[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1167 -1182 .
[9]	Fu Yuechen, Ni Mingkang. The Inner Layer of a Class of Singularly Perturbed High-Order Equations with Discontinuous Right-Hand Side[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1153 -1166 .
[10]	Chai Mengcen, Dai Yuxia. Freely Quasiconformal Mappings in Quasiconvex Metric Spaces[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1127 -1135 .

Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schr $\rm\ddot{o}$ dinger Equation

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 7

References 29

Related Articles 15

Metrics

Comments

Recommended 10

Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schro¨\rm\ddot{o}dinger Equation

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 7

References 29

Related Articles 15

Metrics

Comments

Recommended 10

Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schr $\rm\ddot{o}$ dinger Equation