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Date, Jiro; Sonta, Hiromi; Kase, Katsuo

doi:10.4144/rpsj1954.29.125

Cited by 5 publications

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“…In [21] we used an alternative procedure to get A (1) n Toda solitons. The approach used by us strongly relies on the work [27] where several soliton equations, including the sine-Gordon equation, has been studied. The dynamics of the A (1) n Toda solitons is governed by the following algebraic equations…”

Section: A (1)mentioning

confidence: 99%

Vertex operator representation of the soliton tau functions in the An(1) Toda models by dressing transformations

Belich

Cuba

Paunov

1998

Journal of Mathematical Physics

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We study the relation between the group-algebraic approach and the dressing symmetry one to the soliton solutions of the A (1) n Toda field theory in 1 + 1 dimensions. Originally solitons in the affine Toda models has been found by Olive, Turok and Underwood. Single solitons are created by exponentials of elements which ad-diagonalize the principal Heisenberg subalgebra. Alternatively Babelon and Bernard exploited the dressing symmetry to reproduce the known expressions for the fundamental tau functions in the sine-Gordon model. In this paper we show the equivalence between these two methods to construct solitons in the A (n) n Toda models. *

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Section: A (1)mentioning

confidence: 99%

Vertex operator representation of the soliton tau functions in the An(1) Toda models by dressing transformations

Belich

Cuba

Paunov

1998

Journal of Mathematical Physics

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“…In Sec. 2 we generalize a method to get solitons introduced by Date [23] which is complementary both to the Hirota method [17], [18] and to the ISM [24]. To illustrate the generality of our approach we fix the coupling constant to be real.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, it turns out that the Jost solutions [5], and therefore the elements of the transition matrix, loose their nice analiticity properties as functions on the spectral parameter. In this Section we generalize an elegant method [23] to obtain the A (1) n Toda solitons. It exploites two important features of the soliton solutions: first, due to the vanishing of the reflection coefficient of the auxiliary linear problem, the corresponding Jost solutions are single valued functions on the spectral parameter λ; second, the soliton Jost solutions are uniquely determined by the scattering data related to the discrete spectrum of the underlying Lax operator.…”

mentioning

confidence: 99%

“…It exploites two important features of the soliton solutions: first, due to the vanishing of the reflection coefficient of the auxiliary linear problem, the corresponding Jost solutions are single valued functions on the spectral parameter λ; second, the soliton Jost solutions are uniquely determined by the scattering data related to the discrete spectrum of the underlying Lax operator. Applying the ideas developed in [23] to the A (1) n Toda models, we recover the equations describing the discrete spectrum of the corresponding linear problem, by using a finite order inner automorphism σ of the simple Lie algebra A n . The last has order n + 1 and introduces the so called principal gradation in the affine Lie algebra A (1) n [26].…”

mentioning

confidence: 99%

“…To fix the rest of the coefficients in the expansion (2.32) we shall impose the following relations on w(x, λ) [23] (…”

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A n (1) Toda solitons and the dressing symmetry

Belich

Paunov

1997

Journal of Mathematical Physics

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We present an elementary derivation of the soliton-like solutions in the A (1) n Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N -solitons are calculated. This enables us to obtain explicit expression for the element which by dressing group action, produces a generic soliton solution. In the particular example of monosolitons we suggest a relation to the vertex operator formalism, previously used by Olive, Turok and Underwood. Our results can also be considered as generalization of the approach to the sine-Gordon solitons, proposed

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Monopoles and Baker functions

Ercolani

Sinha

1989

Commun. Math. Phys.

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The work in this paper pertains to the solutions of Nahm's equations, which arise in the Atiyah-Drinfield-Hitchin-Manin-Nahm construction of solutions to the BogomoΓnyi equations for static monopoles. This paper provides an explicit construction of the solution of Nahm's equations which satisfy regularity and reality conditions. The Lax form of Nahm's equations is reduced to a standard eigenvalue problem by a special gauge transformation. These equations may then be solved by the method of Baker-Krichever. This leads to a compact representation of the solutions of Nahm's equations. The regularity condition is shown to be related to the monodromy of the gauge reduced linear operator. Hitchin showed that the solutions of Nahm's equations can be characterized by an algebraic curve and some data on that curve. Here, this characterization reduces to a transcendental equation involving certain loop integrals of a meromorphic differential. Donaldson coordinatized the moduli space of fc-monopoles by a class of rational maps from the Riemann sphere to itself. The data of a Baker function is equivalent to this map. This method gives an "apriori" construction of the (known) two monopole solutions. We also give a generalization of the two monopole solution to a class of elliptic solutions of arbitrary charge. These solutions correspond to reducible curves with elliptic components and the associated Donaldson rational function has a simple partial fraction expansion.

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Cited by 5 publications

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Vertex operator representation of the soliton tau functions in the An(1) Toda models by dressing transformations

Vertex operator representation of the soliton tau functions in the An(1) Toda models by dressing transformations

A n (1) Toda solitons and the dressing symmetry

Monopoles and Baker functions

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