Quantum torus symmetries of the CKP and multi-component CKP hierarchies

Liu, Qiufang; Li, Chuanzhong

doi:10.1063/1.5010927

Cited by 10 publications

(1 citation statement)

References 24 publications

(33 reference statements)

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“…The last research object is the additional symmetries of the CKP hierarchy [5,20,25,37,44]. In this paper, we will be interested in their actions on tau functions.…”

Section: Introductionmentioning

confidence: 99%

CKP hierarchy and free Bosons

Yang,

Geng,

Cheng

2021

Preprint

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In this paper, free Bosons are used to study some integrable properties of the CKP hierarchy, from the aspects of tau functions. Firstly, the modified CKP hierarchy is constructed by using free Bosons and the corresponding Lax structure is given. Then the constrained CKP hierarchy is found to be related with the modified CKP hierarchy, and the corresponding solutions are derived by using free Bosons. Next by using the relations between the Darboux transformations and the squared eigenfunction symmetries, we express the Darboux transformations of the CKP hierarchy in terms of free Bosons, by which one can better understand the essential of the CKP Darboux transformations. In particular, the additional symmetries of the CKP hierarchy can be viewed as the infinitesimal generator of the CKP Darboux transformations. Based upon these results, we finally obtain the actions of the CKP additional symmetries on the CKP tau functions constructed by free Bosons.

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“…The last research object is the additional symmetries of the CKP hierarchy [5,20,25,37,44]. In this paper, we will be interested in their actions on tau functions.…”

Section: Introductionmentioning

confidence: 99%

CKP hierarchy and free Bosons

Yang,

Geng,

Cheng

2021

Preprint

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Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation

Liu

Zhang

2019

Z. Angew. Math. Phys.

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In this paper, a modified symbolic computation approach is proposed. The multiple rogue wave solutions of a generalized (2+1)-dimensional Boussinesq equation are obtained by using the modified symbolic computation approach. Dynamics features of these obtained multiple rogue wave solutions are displayed in 3D and contour plots. Compared with the original symbolic computation approach, our method does not need to find Hirota bilinear form of nonlinear system.

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CKP hierarchy and free bosons

Yang

Geng

Cheng

2021

Journal of Mathematical Physics

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In this paper, free bosons are used to study some integrable properties of Kadomtsev-Petviashvili (KP) hierarchy of C type (CKP hierarchy), from the aspects of tau functions. First, the modified CKP hierarchy is constructed by using free bosons, and the corresponding Lax structure is given. Then, the constrained CKP hierarchy is found to be related to the modified CKP hierarchy, and the corresponding solutions are derived by using free bosons. Next, by using the relations between the Darboux transformations and the squared eigenfunction symmetries, we express the Darboux transformations of the CKP hierarchy in terms of free bosons, by which one can better understand the essential properties of the CKP Darboux transformations. In particular, the additional symmetries of the CKP hierarchy can be viewed as the infinitesimal generator of the CKP Darboux transformations. Based on these results, we finally obtain the actions of the CKP additional symmetries on the CKP tau functions constructed by free bosons.

show abstract

Quantum torus symmetries of the CKP and multi-component CKP hierarchies

Cited by 10 publications

References 24 publications

CKP hierarchy and free Bosons

CKP hierarchy and free Bosons

Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation

CKP hierarchy and free bosons

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