Differential form method for finding symmetries of a (2+1)-dimensional Camassa–Holm system based on its Lax pair

Lv, Na; Mei, Jianqin; Zhang, Hongqing

doi:10.1016/j.chaos.2012.01.010

Cited by 8 publications

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References 21 publications

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“…Edelen developed the theory of the differential form method extensively [12,13], and wrote some computer programs using this technique [14]. Recently, we use the differential form method to seek Lie point symmetries of a (2+1)-dimensional Camassa-Holm (CH) system based on its Lax pair [15]. Based on the discrete exterior differential technique [16,17], the method that proposed by Harrison and Estabrook has been extended to the case of differentialdifference equations [18,19] and difference equations [20], respectively.…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetries of Two (2+1)-Dimensional Toda-Like Lattices by the Extended Differential Form Method

Mei

Zhang

2012

Int. J. Geom. Methods Mod. Phys.

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Based on the extended Harrison and Estabrook's differential form method, we obtain the Lie symmetries of two (2+1)-dimensional Toda-like lattices from two different sets of differential forms, respectively. Moreover it is shown that, for each lattice, the determining equations for the two sets give the same symmetries; and the set of differential forms for the lower-dimensional space can make the computation for finding symmetries simpler than the other.

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Section: Introductionmentioning

confidence: 99%

Lie Symmetries of Two (2+1)-Dimensional Toda-Like Lattices by the Extended Differential Form Method

Mei

Zhang

2012

Int. J. Geom. Methods Mod. Phys.

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“…Кроме того, посредством преобразования взаимности она может быть связана с модифицированной иерархией Кадомцева-Петвиашвили (далее иерархией мКП) [4]. Используя метод дифференциальных форм, авторы работы [5] рассматривали точечные симметрии Ли для системы (1), взяв за основу пару Лакса. После редукции ∂ y = 0 система (1) принимает вид (1 + 1)-мерного уравнения КХ [6], [7]…”

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Obtaining multisoliton solutions of the $(2+1)$-dimensional Camassa-Holm system using Darboux transformations

Мао

Mao

2020

TMF

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Построены и изучаются преобразования Дарбу для $(2+1)$-мерной системы Камассы-Холма. Применяется преобразование взаимности, которое связывает $(2+1)$-мерную систему Камассы-Холма и линейную систему, ассоциированную с модифицированной иерархией Кадомцева-Петвиашвили. С помощью трех операторов преобразования Дарбу получены три типа решений $(2+1)$-мерной системы Камассы-Холма, одно из которых представляет собой многосолитонное решение. Дополнительно вкратце обсуждаются рациональные решения.

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New bilinear Bäcklund transformation with multisoliton solutions for the (2+1)-dimensional Sawada–Kotera model

2013

Nonlinear Dyn

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Differential form method for finding symmetries of a (2+1)-dimensional Camassa–Holm system based on its Lax pair

Cited by 8 publications

References 21 publications

Lie Symmetries of Two (2+1)-Dimensional Toda-Like Lattices by the Extended Differential Form Method

Lie Symmetries of Two (2+1)-Dimensional Toda-Like Lattices by the Extended Differential Form Method

Obtaining multisoliton solutions of the $(2+1)$-dimensional Camassa-Holm system using Darboux transformations

New bilinear Bäcklund transformation with multisoliton solutions for the (2+1)-dimensional Sawada–Kotera model

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