@article {bertola2018painleve,
	title = {Painlev{\'e} IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane},
	journal = {Symmetry, Integrability and Geometry. Methods and Applications},
	volume = {14},
	year = {2018},
	publisher = {National Academy of Sciences of Ukraine},
	abstract = {<p>We study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a transition for a special value of the parameter, where it develops a corner-type singularity. In the double scaling limit near the transition we determine the asymptotic behaviour of the orthogonal polynomials in terms of a solution of the Painlev{\textasciiacute}e IV equation. We determine the Fredholm determinant associated to such solution and we compute it numerically on the real line, showing also that the corresponding Painlev{\textasciiacute}e transcendent is pole-free on a semiaxis.</p>},
	doi = {10.3842/SIGMA.2018.091},
	author = {Marco Bertola and Jos{\'e} Gustavo Elias Rebelo and Tamara Grava}
}
@article {2010,
	title = {Painlev{\'e} II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit},
	journal = {Comm. Pure Appl. Math. 63 (2010) 203-232},
	number = {arXiv.org;0812.4142v1},
	year = {2010},
	publisher = {Wiley},
	abstract = {In the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach.},
	doi = {10.1002/cpa.20277},
	url = {http://hdl.handle.net/1963/3799},
	author = {Tom Claeys and Tamara Grava}
}
