Quasi-Grammian Solutions of the Generalized Coupled Dispersionless Integrable System

Haider, Bushra

doi:10.3842/sigma.2012.084

Cited by 7 publications

(5 citation statements)

References 43 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…тогда простые расчеты приводят к следующему матричному решению Ψ n пары Лакса (1): Подставляя матрицу H n в уравнение (25), получим искомое выражение для матрицы Q…”

Section: явные решенияunclassified

Модель Обобщенного Магнетика Гейзенберга На Решетке И Ее Квазидетерминантные Солитонные Решения

Риаз¹,

Riaz²,

Хассан³

et al. 2018

TMF

View full text Add to dashboard Cite

Section: явные решенияunclassified

Модель Обобщенного Магнетика Гейзенберга На Решетке И Ее Квазидетерминантные Солитонные Решения

Риаз¹,

Riaz²,

Хассан³

et al. 2018

TMF

View full text Add to dashboard Cite

“…In 2012, the Nth-order rogue wave solutions of (1.4) were obtained by virtue of generalized Darboux transformation [29]. With the help of the standard binary Darboux transformation the quasi-Grammian multisoliton solutions of (1.4) are obtained [30].…”

Section: Introductionmentioning

confidence: 99%

Finite-band solutions of the coupled dispersionless hierarchy

Li¹

2016

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The coupled dispersionless hierarchy is derived with the help of the zero curvature equation. Based on the Lax matrix, we introduce an algebraic curve of arithmetic genus n, from which we establish the corresponding meromorphic function ϕ, the Baker–Akhiezer function , and Dubrovin-type equations. The straightening out of all the flows is given under the Abel–Jacobi coordinates. Using the asymptotic properties of ϕ and , we obtain the explicit theta function representations of the meromorphic function ϕ, the Baker–Akhiezer function and of solutions for the whole hierarchy.

show abstract

“…In the present paper, we present a systematic approach to the construction of (1.5) by means of a standard binary Darboux transformation (BDT) and written in terms of quasideterminants [7,8]. Quasideterminants have various useful properties which play important roles in constructing exact solutions of integrable systems [11,12,21,26,34].…”

Section: Introductionmentioning

confidence: 99%

Binary Darboux transformation for the Sasa–Satsuma equation

Nimmo

Yilmaz

2015

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The Sasa-Satsuma equation is an integrable higher-order nonlinear Schrödinger equation. Higher-order and multicomponent generalisations of the nonlinear Schrödinger equation are important in various applications, e.g., in optics. One of these equations is the Sasa-Satsuma equation. We present the binary Darboux transformations for the Sasa-Satsuma equation and then construct its quasigrammians solutions by iterating its binary Darboux transformations. Periodic, one-soliton, two-solitons and breather solutions are given as explicit examples.

show abstract

Quasi-Grammian Solutions of the Generalized Coupled Dispersionless Integrable System

Abstract: Abstract. The standard binary Darboux transformation is investigated and is used to obtain quasi-Grammian multisoliton solutions of the generalized coupled dispersionless integrable system.

Cited by 7 publications

References 43 publications

Модель Обобщенного Магнетика Гейзенберга На Решетке И Ее Квазидетерминантные Солитонные Решения

Модель Обобщенного Магнетика Гейзенберга На Решетке И Ее Квазидетерминантные Солитонные Решения

Finite-band solutions of the coupled dispersionless hierarchy

Binary Darboux transformation for the Sasa–Satsuma equation

Contact Info

Product

Resources

About