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

Kudashev, Vadim R.; Suleimanov, Bulat I.

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

Authors

Description

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: kudashev@imat.rb.ru, bis@imat.rb.ru