Darboux transformation of a semi-discrete coupled dispersionless integrable system

Riaz, H. Wajahat A.; Hassan, M.

doi:10.1016/j.cnsns.2017.01.011

Cited by 29 publications

(4 citation statements)

References 26 publications

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“…DT is one of solution generating technique in soliton theory that allow us to express the solutions for a given integrable equation in simple explicit form [28][29][30][31][32][33]. In this section, we construct the DT of the multicomponent .…”

Section: Darboux Transformationmentioning

confidence: 99%

On soliton solutions of multi-component semi-discrete short pulse equation

Riaz

Hassan

2018

J. Phys. Commun.

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The short pulse (SP) equation is an integrable equation. Multi-component generalizations of the SP equation are important for describing the polarization or anisotropic effects in optical fibers. An integrable semi-discretization of multi-component SP equation via Lax pair and Darboux transformation (DT) has been presented. We derive a Lax pair representation for the multi-component semidiscrete short pulse (sdSP) equation in the form of a block matrices by generalizing the 2×2 Lax pair matrices to the case of 2 2 N Ń . A DT is studied for the multi-component sdSP equation and is used to compute soliton solutions of the system. Further, by expanding quasideterminants, we compute cuspon-soliton, smooth-soliton and loop-soliton solutions of the complex sdSP equation.

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Section: Darboux Transformationmentioning

confidence: 99%

On soliton solutions of multi-component semi-discrete short pulse equation

Riaz

Hassan

2018

J. Phys. Commun.

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“…Преобразование Дарбу является важным способом построения решений солитонных уравнений (см., например, работы [18]- [20]). Далее мы применяем преобразование Дарбу к паре Лакса (2.1), (2.2) и получаем решения уравнения ПДКИ.…”

Section: преобразование дарбуunclassified

Преобразование Дарбу Для Полудискретного Уравнения Коротких Импульсов

Риаз¹,

Riaz²,

Хассан³

et al. 2018

TMF

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Преобразование Дарбу на решениях полудискретного уравнения коротких импульсов выражено через квазидетерминантные матрицы Дарбу. Также для N -петлевого солитонного решения приведена квазидетерминантная формула. Получено общее выражение для многопетлевого решения через квазидетерминанты. С использованием свойства квазидетерминантов найдены явные решения. В качестве примера вычислены в явном виде одно-и двухпетлевые солитонные решения.

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“…Methods have been introduced to solve the NLEEs, including the inverse scattering transformation, Bäcklund transformation (BT), Darboux transformation, Hirota method and Lie symmetry approach [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

et al. 2021

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A (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynam-ics and plasma physics is hereby investigated. Via the Hirota method, bilinear Bäcklund transformation are obtained, along with two types of the analytic solutions. Kink-shaped soliton solutions are derived via the Hirota method. Breather solutions are derived via the extended homoclinic test approach and lump solutions are obtained from the breather solutions under a limiting procedure. We find that the shape and amplitude of the one-kink soliton keep unchanged during the propagation and the velocity of the one-kink soliton depends on all the coefficients in the equation. We graphically demonstrate that the interaction between the two-kink solitons is elastic, and analyse the solitons with the influence of the coefficients. We observe that the amplitudes and shapes of the breather and lump remain unchanged during the propagation, and graphically present the breathers and lumps with the influence of the coefficients in the equation.

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Darboux transformation of a semi-discrete coupled dispersionless integrable system

Cited by 29 publications

References 26 publications

On soliton solutions of multi-component semi-discrete short pulse equation

On soliton solutions of multi-component semi-discrete short pulse equation

Преобразование Дарбу Для Полудискретного Уравнения Коротких Импульсов

Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

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