Nonlinear superposition formula for the Kaup–Kupershmidt partial differential equation

Musette, Micheline; Verhoeven, Caroline

doi:10.1016/s0167-2789(00)00081-6

Cited by 44 publications

(19 citation statements)

References 24 publications

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“…Despite of this close relation, it was noted that some properties of the SK and KK equations are rather different, see e.g. [16]. It seems that distinctions between the lattice analogs of these equations are even more deep.…”

Section: Introductionmentioning

confidence: 99%

Differential–difference equations associated with the fractional Lax operators

Адлер¹,

Postnikov²

2011

J. Phys. A: Math. Theor.

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Abstract. We study integrable hierarchies associated with spectral problems of the form P ψ = λQψ where P, Q are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous generalizations of the Bogoyavlensky type lattices. While the latter turn into the Korteweg-de Vries equation under the continuous limit, the lattices under consideration provide discrete analogs of the SawadaKotera and Kaup-Kupershmidt equations. The r-matrix formulation and several simplest explicit solutions are presented.

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Section: Introductionmentioning

confidence: 99%

Differential–difference equations associated with the fractional Lax operators

Адлер¹,

Postnikov²

2011

J. Phys. A: Math. Theor.

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“…Most recently, Geng, He and Wu constructed the algebro-geometric solutions for the SK hierarchy [15]. For more results and properties of the SK equation, one is referred to [2,11,13,19,20,35,30,37,44,33] and the references there. With Tian, one of the authors proposed a supersymmetric SK equation [41], which reads as…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications

Mao¹,

Liu²,

Xue³

2021

JNMP

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In this paper, we construct a Darboux transformation and the related Bäcklund transformation for the supersymmetric Sawada-Kotera (SSK) equation.The associated nonlinear superposition formula is also worked out. We demonstrate that these are natural extensions of the similar results of the Sawada-Kotera equation and may be applied to produce the solutions of the SSK equation. Also, we present two semi-discrete systems and show that the continuum limit of one of them goes to the SKK equation.

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“…Parker 13,14 obtained the N-soliton solution of SK and KK equation. Musette and Verhoeven 15 achieved the solution of fifth-order KK equations of integrable cases of Henon–Heiles system. Tam and Hu 16 found three Soliton solutions of KK-type equations using Hirota method and Mathematica.…”

Section: Introductionmentioning

confidence: 99%