One-Parametric Family of the Double-Scaling Limits in the Hermitian Matrix Model Φ6: Onset of Nondissipative Shock Waves
Vadim R. Kudashev, Bulat I. Suleimanov
Abstract
We construct a one-parametric family of the double-scaling limits in the hermitian matrix model Φ6 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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