4.5 Article

Quasi-Grammian solutions of the coupled Gerdjikov-Ivanov equation

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

On long-time asymptotics to the nonlocal short pulse equation with the Schwartz-type initial data: Without solitons

Xin Wu et al.

Summary: In this work, we study the initial value problem of the nonlocal short pulse (NSP) equation with Schwartz-type initial data. We discuss the NSP equation using its Lax pair, which includes an infinite number of conservation laws and a finite-dimensional Hamiltonian function. The relevant spectral analysis is discussed separately due to the singularity of the spectrum. A suitable Riemann-Hilbert (RH) problem is established to express the solution of the NSP equation. By using the nonlinear steepest descent method, the original RH problem is transformed into a model RH problem, yielding the long-time asymptotic solution of the NSP equation.

PHYSICA D-NONLINEAR PHENOMENA (2023)

Article Physics, Multidisciplinary

Soliton Resolution for the Wadati-Konno-Ichikawa Equation with Weighted Sobolev Initial Data

Zhi-Qiang Li et al.

Summary: In this study, we employ the partial derivative-steepest descent method to investigate the Cauchy problem of the WKI equation with initial conditions in weighted Sobolev space H(R). The long time asymptotic behavior of the solution is derived, and based on this behavior, we prove the soliton resolution conjecture of the WKI equation.

ANNALES HENRI POINCARE (2022)

Article Mathematics, Applied

Riemann-Hilbert problem for the focusing nonlinear Schrodinger equation with multiple high-order poles under nonzero boundary conditions

Jin-Jie Yang et al.

Summary: The Riemann-Hilbert problem is developed to study the focusing behavior of the nonlinear Schrodinger equation with multiple high-order poles. By employing Laurent expansion and solving an algebraic system, soliton solutions corresponding to the transmission coefficient are obtained.

PHYSICA D-NONLINEAR PHENOMENA (2022)

Article Mathematics

Soliton resolution for the complex short pulse equation with weighted Sobolev initial data in space-time solitonic regions

Zhi-Qiang Li et al.

Summary: In this work, we employ the (partial derivative) over bar -steepest descent method to investigate the Cauchy problem of the complex short pulse (CSP) equation with initial conditions in weighted Sobolev space H(R). Firstly, we successfully derive the Hamiltonian function of the CSP equation based on its Lax pair. Furthermore, the long time asymptotic behavior of the solution u(x, t) is derived in a fixed space-time cone S(y(1), y(2), v(1), v(2)) ={(y, t) is an element of R-2: y = y(0) + vt, y(0) is an element of [y(1),y(2)], v is an element of [v(1), v(2)]}. On the basis of the resulting asymptotic behavior, we prove the soliton resolution conjecture of the CSP equation which includes the soliton term confirmed by N(I)-soliton on discrete spectrum and the t(-1/2) order term on continuous spectrum with residual error up to O(t(-1)). (C) 2022 Elsevier Inc. All rights reserved.

JOURNAL OF DIFFERENTIAL EQUATIONS (2022)

Article Acoustics

Binary Darboux transformation for the Gerdjikov-Ivanov equation

Halis Yilmaz

Summary: This paper presents a standard binary Darboux transformation for the Gerdjikov-Ivanov equation and constructs its quasigrammian solutions. Furthermore, it provides examples of multi-soliton, breather, and rogue wave solutions for the Gerdjikov-Ivanov equation.

WAVE MOTION (2022)

Article Mathematics

On the soliton resolution and the asymptotic stability of N-soliton solution for the Wadati-Konno-Ichikawa equation with finite density initial data in space-time solitonic regions

Zhi-Qiang Li et al.

Summary: This work investigates the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with finite density initial data in space-time solitonic regions. By analyzing the Lax spectrum problem and the corresponding Riemann-Hilbert problem, the leading order approximation to the solution of the WKI equation is derived. The asymptotic approximation of the WKI equation is characterized by soliton terms on discrete spectrum and a leading order term on continuous spectrum, with residual error up to O(t^(-3/4)). The results also confirm the soliton resolution conjecture and the asymptotic stability of the N-soliton solution for the WKI equation with finite density initial data.

ADVANCES IN MATHEMATICS (2022)

Article Mathematics, Applied

Coupled derivative nonlinear Schrodinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber

Yunyun Zhai et al.

Summary: The N-fold generalized Darboux transformation for the cDNLSIII equation is constructed in this paper, leading to general higher-order rogue wave solutions with applications in nonlinear fiber communication. The interactions between rogue waves and solitons or breathers are explored, along with the analysis of their features.

APPLIED MATHEMATICS AND COMPUTATION (2021)

Article Mathematics, Applied

Some localized wave solutions for the coupled Gerdjikov-Ivanov equation

Min-Jie Dong et al.

Summary: This paper investigates the coupled Gerdjikov-Ivanov equation and its important role in theoretical physics, obtaining localized waves through various mathematical methods. It has significant implications for theoretical experiments on the rogue wave generation mechanism and propagation trajectory.

APPLIED MATHEMATICS LETTERS (2021)

Article Mathematics, Applied

Binary Darboux transformation and soliton solutions for the coupled complex modified Korteweg-de Vries equations

Yi Zhang et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2020)

Article Physics, Multidisciplinary

Soliton solutions of noncommutative anti-self-dual Yang-Mills equations

Claire R. Gilson et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2020)

Article Physics, Multidisciplinary

Exact multisolitons of noncommutative and commutative Lakshmanan-Porsezian-Daniel equation

H. Wajahat A. Riaz

EUROPEAN PHYSICAL JOURNAL PLUS (2020)

Article Mathematics, Applied

Riemann-Hilbert method and N-soliton for two-component Gerdjikov-Ivanov equation

Yongshuai Zhang et al.

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS (2017)

Article Mathematics, Applied

Binary Darboux transformation for the coupled Sasa-Satsuma equations

Hai-Qiang Zhang et al.

Article Physics, Multidisciplinary

Binary Darboux transformation for the Sasa-Satsuma equation

Jonathan J. C. Nimmo et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2015)

Article Mathematics, Applied

Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations

Halis Yilmaz

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS (2015)

Article Physics, Multidisciplinary

The higher order rogue wave solutions of the Gerdjikov-Ivanov equation

Lijuan Guo et al.

PHYSICA SCRIPTA (2014)

Article Mathematics, Applied

On Darboux transformations for the derivative nonlinear Schrodinger equation

Jonathan J. C. Nimmo et al.

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS (2014)

Article Physics, Mathematical

The rogue wave and breather solution of the Gerdjikov-Ivanov equation

Shuwei Xu et al.

JOURNAL OF MATHEMATICAL PHYSICS (2012)

Article Physics, Fluids & Plasmas

Nonlinear Schrodinger equation: Generalized Darboux transformation and rogue wave solutions

Boling Guo et al.

PHYSICAL REVIEW E (2012)

Article Physics, Multidisciplinary

Quasideterminant Solutions of a Noncommutative Nonisospectral Kadomtsev-Petviashvili Equation

Zhu Xiao-Ming et al.

COMMUNICATIONS IN THEORETICAL PHYSICS (2011)

Article Physics, Multidisciplinary

Sato-theoretic construction of solutions to noncommutative integrable systems

Kenichi Kondo

PHYSICS LETTERS A (2011)

Article Physics, Multidisciplinary

Noncommutative Toda chains, Hankel quasideterminants and the Painleve II equation

Vladimir Retakh et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2010)

Article Physics, Multidisciplinary

Dromion solutions of noncommutative Davey-Stewartson equations

C. R. Gilson et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2009)

Article Physics, Multidisciplinary

Waves that appear from nowhere and disappear without a trace

N. Akhmediev et al.

PHYSICS LETTERS A (2009)

Article Physics, Multidisciplinary

On a direct approach to quasideterminant solutions of a noncommutative KP equation

C. R. Gilson et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2007)

Article Mathematics

Quasideterminants

I Gelfand et al.

ADVANCES IN MATHEMATICS (2005)

Article Mathematics, Applied

Soliton interactions in the vector NLS equation

MJ Ablowitz et al.

INVERSE PROBLEMS (2004)

Article Physics, Multidisciplinary

Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation

EG Fan

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2000)

Article Physics, Multidisciplinary

Applications of Darboux transformations to the self-dual Yang-Mills equations

JJC Nimmo et al.

THEORETICAL AND MATHEMATICAL PHYSICS (2000)