One-Parametric Family of the Double-Scaling Limits in the Hermitian Matrix Model $Φ^6:$ Onset of Nondissipative Shock Waves

Vadim R. Kudashev; Bulat I. Suleimanov

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arXiv · hep-th/9811007

One-Parametric Family of the Double-Scaling Limits in the Hermitian Matrix Model $Φ^6:$ Onset of Nondissipative Shock Waves

Vadim R. Kudashev·Bulat I. Suleimanov

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Abstract

We construct a one-parametric family of the double-scaling limits in the hermitian matrix model $Φ^6$ for 2D quantum gravity. The known limit of Bresin, Marinari and Parisi belongs to this family. The family is represented by the Gurevich-Pitaevskii solution of the Korteveg-de Vries equation which describes the onset of nondissipative shock waves in media with small dispersion. Numerical simulation of the universal Gurevich-Pitaevskii solution is made.

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Vadim R. Kudashev, Bulat I. Suleimanov. 1998-11-02. One-Parametric Family of the Double-Scaling Limits in the Hermitian Matrix Model $Φ^6:$ Onset of Nondissipative Shock Waves. https://arxiv.org/abs/hep-th/9811007

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