ﻻ يوجد ملخص باللغة العربية
We derive a class of equations of state for a multi-phase thermodynamic system associated with a finite set of order parameters that satisfy an integrable system of hydrodynamic type. As particular examples, we discuss one-phase systems such as the van der Waals gas and the effective molecular field model. The case of N-phase systems is also discussed in detail in connection with entropies depending on the order parameter according to Tsallis composition rule.
In the first part of the paper, we classify linear integrable (multi-dimensionally consistent) quad-equations on bipartite isoradial quad-graphs in $mathbb C$, enjoying natural symmetries and the property that the restriction of their solutions to th
We consider the generic quadratic first integral (QFI) of the form $I=K_{ab}(t,q)dot{q}^{a}dot{q}^{b}+K_{a}(t,q)dot{q}^{a}+K(t,q)$ and require the condition $dI/dt=0$. The latter results in a system of partial differential equations which involve the
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in
The notion of monodromy was introduced by J. J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant was extensively studied since then and was shown to be non-trivial in
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero temperature