Symmetries in the third Painlevé equation arising from the modified Pohlmeyer-Lund-Regge hierarchy

Kikuchi, Tetsuya

doi:10.1063/1.3658862

Cited by 1 publication

(3 citation statements)

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“…We developed the algebraic dressing method for the KN hierarchy and several relations found previously in the literature emerge naturally. For instance, the form of the gauge transformations linking the three DNLSEs and the precise connection between the solutions of (35) and those of (26). Moreover, the weight function introduced in the revised IST [10] also arises from the algebraic dressing method.…”

Section: Discussionmentioning

confidence: 99%

“…Using (67) we have a solution of (24), that with the appropriate reduction yields a solution of (26) with the plus sign, whose square modulus reads…”

Section: Two-vertex Solutionmentioning

confidence: 99%

“…We will explain precisely the origin of this relation. Equation (7) was also referred as the modified Pohlmeyer-Lund-Regge model [26] and it can be reduced to the third Painlevé equation.…”

Section: Introductionmentioning

confidence: 99%

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The algebraic structure behind the derivative nonlinear Schrödinger equation

França¹,

Gomes²,

Zímerman³

2013

J. Phys. A: Math. Theor.

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The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of aŝ 2 Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows, respectively. The equivalence between the latter and the massive Thirring model is explicitly demonstrated also. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation.

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Section: Discussionmentioning

confidence: 99%

“…Using (67) we have a solution of (24), that with the appropriate reduction yields a solution of (26) with the plus sign, whose square modulus reads…”

Section: Two-vertex Solutionmentioning

confidence: 99%