Interest to the tasks by bound with systems of the quasilinear equations recently has revived. Therefore we have decided to expose in electronic sort our operation published in Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 2, pp. 189-199, November, 1994. Original article submitted October 26, 1993. Exact single-wave and two-wave solutions of systems of equations of th...

We use Elie Cartan's method of equivalence to give a complete classification, in terms of differential invariants, of second-order ordinary differential equations admitting Lie groups of fibre-preserving point symmetries. We then apply our results to the determination of all second-order equations which are equivalent, under fibre-preserving transformations, to the free particle equation. In ad...

We prove the existence of the double scaling limit for unitary invariant ensembles of random matrices with non analytic potentials. The limiting reproducing kernel is expressed in terms of solutions of the Dirac system of differential equations with a potential defined by the Hastings-McLeod solution of the Painleve II equation. Our approach is based on the construction of the perturbation expa...

In this paper, we present explicit Painlevé test for the potential Boussinesq equation, The murrary equation, The (2 + 1) Calogero equation, The Rosenau – Hyman equation (RH), Cole – Hopf (CH) equation, The Fornberg – Whitham equation (FW), Some of these equations have shown to possess Painlevé property, therefore, are Painleve integrable while the rest did not pass the test and reasons for tha...

6.6). In [3, 31, 321 Wu, McCoy, Tracy, and Barouch (WMTB) discovered that the scaled two point functions for the two-dimensional Ising model are expressible in terms of a Painled function of the third kind. This discovery was made by using results from the thesis of Myers [21] (which was in part based upon earlier work by Latta [16]) who established a connection between a linear integral equati...