@article {2010,
	title = {Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit},
	journal = {SIAM J. Math. Anal. 42 (2010) 2132-2154},
	number = {SISSA;09/2010/FM},
	year = {2010},
	abstract = {We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.},
	doi = {10.1137/090779103},
	url = {http://hdl.handle.net/1963/3839},
	author = {Tamara Grava and Tom Claeys}
}
@article {2004,
	title = {Singular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation},
	journal = {Int. Math. Res. Not. 2004, no. 32, 1619-1683},
	number = {arXiv.org;math-ph/0306050},
	year = {2004},
	abstract = {We are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the Szego kernel of certain Riemann surfaces branched over the given 2m+2 points. These Riemann surfaces are constructed from a permutation representation of the symmetric group S_N to which the quasi-permutation monodromy representation has been reduced. The permutation representation of our problem generates the cyclic subgroup Z_N. For this reason the corresponding Riemann surfaces of genus N(m-1) have Z_N symmetry. This fact enables us to write the matrix entries of the solution of the NxN Riemann-Hilbert problem as a product of an algebraic function and theta-function quotients. The algebraic function turns out to be related to the Szego kernel with zero characteristics. From the solution of the Riemann- Hilbert problem we automatically obtain a particular solution of the Schlesinger system. The tau-function of the Schlesinger system is computed explicitly. The rank 3 problem with four singular points (0,t,1,\\\\infty) is studied in detail. The corresponding solution of the Riemann-Hilbert problem and the Schlesinger system is given in terms of Jacobi\\\'s theta-function with modulus T=T(t), Im(T)>0. The function T=T(t) is invertible if it belongs to the Siegel upper half space modulo the subgroup \\\\Gamma_0(3) of the modular group. The inverse function t=t(T) generates a solution of a general Halphen system.},
	doi = {10.1155/S1073792804132625},
	url = {http://hdl.handle.net/1963/2540},
	author = {Victor Z. Enolski and Tamara Grava}
}
