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

paper

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

arXiv:hep-th/9811007

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.

8 pages, latex, 20k; e-mail: [email protected], [email protected]

One-Parametric Family of the Double-Scaling Limits in the Hermitian Matrix Model Φ6: Onset of Nondissipative Shock Waves

Abstract

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