Nucleosynthesis Constraint on Cosmic Strings with the Scaling Law

Koikawa, Takao

doi:10.1143/ptp.85.1049

Cited by 25 publications

(34 citation statements)

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“…For this purpose other methods may be used. One of the most powerful methods would be the inverse scattering method [26], which was applied to a five-dimensional string theory system [27] and static five-dimensional cases [28].…”

Section: Discussionmentioning

confidence: 99%

New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness

Mishima¹,

Iguchi²

2006

AIP Conference Proceedings

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New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are obtained by using solitonic solution-generating techniques. The new solutions are shown to be equivalent to the four-dimensional multisolitonic solutions derived from particular class of four-dimensional Weyl solutions and to include different black rings from those obtained by Emparan and Reall.

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Section: Discussionmentioning

confidence: 99%

New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness

Mishima¹,

Iguchi²

2006

AIP Conference Proceedings

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“…We showed how we obtain a continuous soliton hierarchy as in the KdV equation case starting with the NCZC(noncommutative zero-curvature) equation [4]. However, we did not show an associated equation for the Toda equation which is known to be a discrete soliton equation.…”

Section: Introductionmentioning

confidence: 81%

“…It is known that the inverse scattering method in the soliton equation is nothing but a zero-curvature equation using the lie algebra valued potentials [6,7]. We proposed to use the "zero-curvature equation" to derive soliton equations where the commutator is replaced by the Moyal bracket [4]. The potentials are not lie algebra valued but a function of four variables.…”

Section: Formulationsmentioning

confidence: 99%

Discrete soliton equation hierarchy

Koikawa¹

2013

AIP Conference Proceedings

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Abstract. It is known that the continuous soliton equations such as the KdV equation have hierarchy structures. A higher order KdV equation constituting the hierarchy includes higher order derivative terms in the equation. The Toda equation is characterized by discreteness in the space dimension. In the hierarchy for the discrete soliton equation such as the Toda equation, neither spatial derivatives nor higher order spatial derivatives appear. Despite of this difference, we show both continuous and discrete soliton equation hierarchies starting with the noncommutative zero curvature equation. Especially, we show the explicit form of the higher order Toda equation.

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“…In the Moyal quantization, the parameter appearing there is the Planch constant that is a unit of spacing between energy levels. In the present case, the parameter k is the spacing between the adjacent particles on the lattice [5].…”

Section: Prhep Unesp2002mentioning

confidence: 99%

Soliton equations by the noncommutative zero curvature formulation

Koikawa¹

2002

Proceedings of Workshop on Integrable Theories, Solitons and Duality — PoS(unesp2002)

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Defining the noncommutative zero-curvature equation, we show that many soliton equations can be written in this form. We demonstrate this by showing that various soliton equations are derived from this equation. The derived soliton equations differ according to different choices of manifolds in the reduction of the noncommutative zero-curvature equation.The Moyal quantization is known to give an alternative to the quantization. Lately people are interested in noncommutative space-time, which is also formulated in the same way as the Moyal quantization [1]. The Moyal quantization expresses quantum theory not by operators but by functions of the phase space. The purpose of this note is to show that the noncommutative zero-curvature equation, which is defined by using the product, can be an alternative to the zero-curvature equation of the matrix-valued potentials.The soliton equations can be formulated in various ways, and one of which is the AKNS formulation [3,4]. This is regarded as the geometrical zero-curvature equation. This is given bywhere A µ = A µ (x 0 , x 1 ; ζ), (µ = 0, 1) are the Lie-algebra valued matrices. These potentials include a parameter ζ, and the specific expansion in terms of the parameter yields a corresponding soliton equation. We define the product by(2) * Speaker.

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Nucleosynthesis Constraint on Cosmic Strings with the Scaling Law

Cited by 25 publications

References 0 publications

New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness

New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness

Discrete soliton equation hierarchy

Soliton equations by the noncommutative zero curvature formulation

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