%0 Journal Article %J Comm. Math. Phys. %D 2017 %T Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation %A Marco Bertola %A Alexander Tovbis %B Comm. Math. Phys. %V 354 %P 525–547 %G eng %U http://dx.doi.org/10.1007/s00220-017-2895-9 %R 10.1007/s00220-017-2895-9 %0 Journal Article %J Phys. Rev. Lett. %D 2017 %T Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation %A Tikan, Alexey %A Billet, Cyril %A Gennady El %A Alexander Tovbis %A Marco Bertola %A Sylvestre, Thibaut %A Gustave, Francois %A Randoux, Stephane %A Genty, Goëry %A Suret, Pierre %A Dudley, John M. %B Phys. Rev. Lett. %I American Physical Society %V 119 %P 033901 %8 Jul %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.033901 %R 10.1103/PhysRevLett.119.033901 %0 Journal Article %J SIGMA Symmetry Integrability Geom. Methods Appl. %D 2016 %T On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight %A Marco Bertola %A Alexander Tovbis %B SIGMA Symmetry Integrability Geom. Methods Appl. %V 12 %P Paper No. 118, 50 pages %G eng %U http://dx.doi.org/10.3842/SIGMA.2016.118 %R 10.3842/SIGMA.2016.118 %0 Journal Article %J Proc. A. %D 2016 %T Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation %A Marco Bertola %A Gennady El %A Alexander Tovbis %B Proc. A. %V 472 %P 20160340, 12 %G eng %U http://dx.doi.org/10.1098/rspa.2016.0340 %R 10.1098/rspa.2016.0340 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2016 %T On Sobolev instability of the interior problem of tomography %A Marco Bertola %A Alexander Katsevich %A Alexander Tovbis %B Journal of Mathematical Analysis and Applications %G eng %0 Journal Article %J Constr. Approx. %D 2015 %T Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation %A Marco Bertola %A Alexander Tovbis %B Constr. Approx. %V 41 %P 529–587 %G eng %U http://dx.doi.org/10.1007/s00365-015-9288-0 %R 10.1007/s00365-015-9288-0 %0 Journal Article %J Anal. Math. Phys. %D 2015 %T Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves %A Marco Bertola %A Alexander Tovbis %B Anal. Math. Phys. %V 5 %P 1–22 %G eng %U http://dx.doi.org/10.1007/s13324-014-0088-7 %R 10.1007/s13324-014-0088-7 %0 Journal Article %J Comm. Pure Appl. Math. %D 2014 %T Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach %A Marco Bertola %A Alexander Katsevich %A Alexander Tovbis %B Comm. Pure Appl. Math. %G eng %0 Journal Article %J Proc. Amer. Math. Soc. %D 2013 %T Inversion formulae for the $\romancosh$-weighted Hilbert transform %A Marco Bertola %A Katsevich, A. %A Alexander Tovbis %B Proc. Amer. Math. Soc. %V 141 %P 2703–2718 %G eng %U http://dx.doi.org/10.1090/S0002-9939-2013-11642-4 %R 10.1090/S0002-9939-2013-11642-4 %0 Journal Article %J Comm. Pure Appl. Math. %D 2013 %T Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I %A Marco Bertola %A Alexander Tovbis %B Comm. Pure Appl. Math. %V 66 %P 678–752 %G eng %U http://dx.doi.org/10.1002/cpa.21445 %R 10.1002/cpa.21445 %0 Journal Article %J Int. Math. Res. Not. IMRN %D 2010 %T Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve %A Marco Bertola %A Alexander Tovbis %B Int. Math. Res. Not. IMRN %P 2119–2167 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196 %R 10.1093/imrn/rnp196