@article {10978,
	title = {On critical behaviour in systems of Hamiltonian partial differential equations},
	year = {2013},
	institution = {SISSA},
	abstract = {<p>We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.</p>},
	author = {Boris Dubrovin and Tamara Grava and Christian Klein and Antonio Moro}
}
@article {2012,
	title = {Thermodynamic phase transitions and shock singularities},
	journal = {Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719},
	number = {arXiv:1107.0394;},
	year = {2012},
	publisher = {The Royal Society},
	abstract = {We show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed.},
	doi = {10.1098/rspa.2011.0459},
	url = {http://hdl.handle.net/1963/6090},
	author = {Giuseppe De Nittis and Antonio Moro}
}
