Publications
Integrability, exact reductions and special solutions of the KP-Whitham equations
G.Biondini
M.A. Hoefer
A. Moro
The KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, is studied. The so-called soliton and harmonic wave limits of the KP-Whitham system are considered, in which two of the Riemann-type dependent variables coincide, giving rise in each case to a four-component (2+1)-dimensional hydrodynamic system. In both of these cases, it is shown that a suitable change of dependent variables splits the resulting four-component system into two parts: (i) a decoupled, independent two-component system comprised of the dispersionless KP equation, (ii) an auxiliary two-component system, coupled to the mean flow equations, which describes either the evolution of a linear wave or a soliton propagating on top of the mean flow. The integrability of both of these four-component systems is then studied, and it is shown that, by applying the Haantjes tensor test as well as the method of hydrodynamic reductions, both systems are completely integrable. Various exact reductions of these systems are then presented which correspond to concrete physical scenarios
Integrability, exact reductions and special solutions of the KP-Whitham equations
G.Biondini
M.A. Hoefer
A. Moro
The KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, is studied. The so-called soliton and harmonic wave limits of the KP-Whitham system are considered, in which two of the Riemann-type dependent variables coincide, giving rise in each case to a four-component (2+1)-dimensional hydrodynamic system. In both of these cases, it is shown that a suitable change of dependent variables splits the resulting four-component system into two parts: (i) a decoupled, independent two-component system comprised of the dispersionless KP equation, (ii) an auxiliary two-component system, coupled to the mean flow equations, which describes either the evolution of a linear wave or a soliton propagating on top of the mean flow. The integrability of both of these four-component systems is then studied, and it is shown that, by applying the Haantjes tensor test as well as the method of hydrodynamic reductions, both systems are completely integrable. Various exact reductions of these systems are then presented which correspond to concrete physical scenarios
Integrability, exact reductions and special solutions of the KP-Whitham equations
G.Biondini
M.A. Hoefer
A. Moro
The KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, is studied. The so-called soliton and harmonic wave limits of the KP-Whitham system are considered, in which two of the Riemann-type dependent variables coincide, giving rise in each case to a four-component (2+1)-dimensional hydrodynamic system. In both of these cases, it is shown that a suitable change of dependent variables splits the resulting four-component system into two parts: (i) a decoupled, independent two-component system comprised of the dispersionless KP equation, (ii) an auxiliary two-component system, coupled to the mean flow equations, which describes either the evolution of a linear wave or a soliton propagating on top of the mean flow. The integrability of both of these four-component systems is then studied, and it is shown that, by applying the Haantjes tensor test as well as the method of hydrodynamic reductions, both systems are completely integrable. Various exact reductions of these systems are then presented which correspond to concrete physical scenarios
Integrability, exact reductions and special solutions of the KP-Whitham equations
G.Biondini
M.A. Hoefer
A. Moro
The KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, is studied. The so-called soliton and harmonic wave limits of the KP-Whitham system are considered, in which two of the Riemann-type dependent variables coincide, giving rise in each case to a four-component (2+1)-dimensional hydrodynamic system. In both of these cases, it is shown that a suitable change of dependent variables splits the resulting four-component system into two parts: (i) a decoupled, independent two-component system comprised of the dispersionless KP equation, (ii) an auxiliary two-component system, coupled to the mean flow equations, which describes either the evolution of a linear wave or a soliton propagating on top of the mean flow. The integrability of both of these four-component systems is then studied, and it is shown that, by applying the Haantjes tensor test as well as the method of hydrodynamic reductions, both systems are completely integrable. Various exact reductions of these systems are then presented which correspond to concrete physical scenarios
Thermodynamic Limit and Dispersive Regularisation in Random Matrix Models
C. Benassi
A. Moro
Phys. Rev. E 101, 052118 (2020)
We show that Hermitian Matrix Models support the occurrence of a new type of phase transition characterised by dispersive regularisation of the order parameter near the critical point. Using the identification of the partition function with a solution of a reduction of the Toda hierarchy, known as Volterra system, we argue that the singularity is resolved via the onset of a multi-dimensional dispersive shock described by an integrable flow in the space of coupling constants. This analysis explains the origin and mechanism leading to the emergence of chaotic behaviours observed in M^6 matrix models and extends its validity to even nonlinearity of arbitrary order.
Exact analysis of phase transitions in mean-field Potts models
P. Lorenzoni
A. Moro
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free energy, in the thermodynamic limit, follows from its semiclassical limit. Analysis of singularities of the equations of state reveals the occurrence of phase transitions of nematic type at not zero external fields and allows for an interpretation of the phase transitions in terms of shock dynamics in the space of thermodynamic variables. The approach is shown at work in the case of a q-state model for q=3 but the method generalizes to arbitrary q. Critical asymptotics of magnetization, susceptibility, specific heat and relative critical exponents β, γ, and α are also provided.