Recent publications

• T. Grava, T. Kriecherbauer, K. Mazzucca, K.D.T.-R. Mc Laughlin, Correlation functions for a chain of short range oscillators Submitted to Journal to Statistical Physics.
• M. Gisonni, T. Grava, G. Ruzza Jacobi Ensemble, Hurwitz numbers and Wilson polynomials, Submitted to Lett. Math. Physics
• T. Grava, A. Maspero, G. Mazzuca, A. Ponno, Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit, Comm. Math. Phys. 380(2) (2020), p.811-851.
• T. Grava, A. Minakov On the long time asymptotic behavior of the modified Korteweg de Vries equation with step-like initial data, to appear in SIAM Journal on Math. Analysis
• M. Girotti, T. Grava, R. Jenkins, Ken D. T. -R. McLaughlin Rigorous asymptotics of a KdV soliton gas , to appear in CMP
• M. Gisonni, T. Grava, G. Ruzza, Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals, Annales Henri Poincare, 21 (2020), 3285-3339.
• E. Basor, P. Bleher, R. Buckingham, T. Grava, A. Its, E. Its, J. Keating,A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions. Nonlinearity,32 (2019), no. 10, 4033–4078
• Bertola, Marco; Elias Rebelo, José Gustavo; Grava, Tamara Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane. SIGMA Symmetry Integrability Geom. Methods Appl. 14 (2018), Paper No. 091, 34 pp.
  
• Grava, T.; Klein, C.; Pitton, G. Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves. Proc. A. 474 (2018), no. 2210, 20170458, 20 pp.
• Balogh, F.; Grava, T.; Merzi, D. Orthogonal polynomials for a class of measures with discrete rotational symmetries in the complex plane. Constr. Approx. 46 (2017), no. 1, 109–169.
• Eggers, J.; Grava, T.; Herrada, M. A.; Pitton, G. Spatial structure of shock formation. J. Fluid Mech. 820 (2017), 208–231.
• Grava, T.; Its, A.; Kapaev, A.; Mezzadri, F. On the Tracy-Widomβ distribution for β=6. SIGMA Symmetry Integrability Geom. Methods Appl. 12 (2016), Paper No. 105, 26 pp.
• T. Grava, Whitham modulation equations and application to small dispersion asymptotics and long time asymptotics of nonlinear dispersive equations, Chapter in Rogue and Shock Waves in Nonlinear Dispersive Media, Lecture Notes in Physics 926, p. 309-335  2016.
• T. Grava, C. Klein, J. Eggers Shock formation in the dispersionless Kadomtsev-Petviashvili equation. Physica D 333, (2016) 157 - 170.
• 333, (2016) 157 - 170.
• B. Dubrovin, T.Grava,T.; Klein, On critical behaviour in generalized Kadomtsev--Petviashvili equations. Nonlinearity 29 (2016) 1384 - 1416.
• F. Balogh, T. Grava, D. Merzi, Orhtogonal polynomials for a class of potentials with discrete rotational symmetries.  Constructive Approximation  46, (2017), 109-169.
• B. Dubrovin, T.Grava, C.Klein, A. Moro, On critical behaviour in systems of Hamiltonian partial differential equations. J. Nonlinear Sci. 25 (2015), no. 3, 631 - 707.
• Claeys, T.; Grava, T.; McLaughlin, K. D. T.-R. Asymptotics for the partition function in two-cut random matrix models. Comm. Math. Phys. 339 (2015), no. 2, 513 - 587.
• T. Grava, A. Kapaev, C. Klein, On the tritronquee solutions of P2I. Constr. Approx. 41 (2015), no. 3, 425 - 466.
• T. Claeys, T. Grava, Critical asymptotic behavior for the Korteweg-de Vries equation and in random matrix theory. Random matrix theory, interacting particle systems, and integrable systems, 71 - 92, Math. Sci. Res. Inst. Publ., 65, Cambridge Univ. Press, New York, 2014.
• T. Grava, T.; C.Klein, A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions. Phys. D 241 (2012), no. 23-24, 2246 - 2264.
• T.Claeys, T.Grava The KdV hierarchy: universality and a Painleve transcendent Int. Math. Res. Not. IMRN 2012, no. 22, 5063 - 5099.
• B. Dubrovin, T. Grava, C. Klein Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations SIAM J. Appl. Math. 71 (2011), no. 4, 983 - 1008.
• T.Claeys, T.Grava, Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit. SIAM J. Math. Analysis, vol 42, p. 2132-2154, 2010.
• S. Abenda, T. Grava, C. Klein, Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions. SIAM J. Appl. Math. vol 70, p 2797-2821, 2010.
• T. Claeys, T. Grava, Painleve II Asymptotics near the Leading Edge of the Oscillatory Zone for the Korteweg de Vries Equation in the Small-Dispersion Limit. Comm. Pure and Appl. Math. 63, (2010) p. 203- 232.
• T. Claeys and T. Grava, Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach. Comm. Math. Phys. 286 (2009), no. 3, 979--1009.
• B. Dubrovin, T. Grava, C. Klein, On universality of critical behaviour in the focusing nonlinear Schroedinger equation, elliptic umbilic catastrophe and the tritronquee solution to the Painleve-I equation. J. Nonlinear Sci. 19 (2009), no. 1, 57--94.
• T. Grava, V.U.Pierce, Fei-Ran Tian, Initial value problem of the Whitham equations for the Camassa-Holm equation. Physica D, 238, (2009) 1, 55--66.
• T. Grava, C. Klein, Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painleve-II equation, Proc. R. Soc. A (2008) n.464, 733- 757.
• T. Grava, C. Klein, Numerical solution of the small dispersion limit of Korteweg - de Vries and Whitham equations, Communications on Pure and Applied Mathematics, 60, (2007), n.11, 1623-1664.
• S. Abenda and T. Grava, Reciprocal transformations and flat metrics on Hurwitz spaces J. Phys. A: Math. Theor. 40 No 35 (2007) 10769-10790.
• T. Grava, Fei-Ran Tian, Large parameter behavior of equilibrium measures. Commun. Math. Sci. 4 (2006), no. 3, 551--573.
• T. Grava, Partition function for multi-cut matrix models J. Phys. A: Math. Gen. 39 No 28 (2006) 8905-8919.
• V. Z.Enolski, T.Grava, Thomae type formulae for singular Z_N curves. Lett. Math. Phys. 76 (2006), no. 2-3, 187--214.
• T. Grava, Partition function for multi-cut matrix models. J. Phys. A 39 (2006), no. 28, 8905–8919.
• Enolskii, V.; Grava, T. Riemann-Hilbert problem and algebraic curves. Bilinear integrable systems: from classical to quantum, continuous to discrete, 65–76, NATO Sci. Ser. II Math. Phys. Chem., 201, Springer, Dordrecht, 2006.
• Grava, T.; Tian, Fei-Ran Large parameter behavior of equilibrium measures. Commun. Math. Sci. 4 (2006), no. 3, 551–573.
• Abenda, S.; Grava, T.; Klein, C. On Whitham equations for Camassa-Holm. "WASCOM 2005''—13th Conference on Waves and Stability in Continuous Media, 1–6, World Sci. Publ., Hackensack, NJ, 2006.
• Abenda, Simonetta; Grava, Tamara Modulation of Camassa-Holm equation and reciprocal transformations. Ann. Inst. Fourier (Grenoble) 55 (2005), no. 6, 1803–1834.
• Grava, Tamara Whitham equations, Bergmann kernel and Lax-Levermore minimizer. Acta Appl. Math. 82 (2004), no. 1, 1–86.
• Enolski, V. Z.; Grava, T. Singular ZN-curves and the Riemann-Hilbert problem. Int. Math. Res. Not. 2004, no. 32, 1619–1683.
• Enolski, V.; Grava, T. On the algebro-geometric solution of 3×3 matrix Riemann-Hilbert problem. SPT 2002: Symmetry and perturbation theory (Cala Gonone), 34–41, World Sci. Publ., River Edge, NJ, 2002.
• Chen, Yang; Grava, Tamara Eigenvalue correlations on hyperelliptic Riemann surfaces. J. Phys. A 35 (2002), no. 4, L45–L49.
• Grava, Tamara Riemann-Hilbert problem for the small dispersion limit of the KdV equation and linear overdetermined systems of Euler-Poisson-Darboux type. Comm. Pure Appl. Math. 55 (2002), no. 4, 395–430.
• Grava, Tamara; Tian, Fei-Ran The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit. Comm. Pure Appl. Math. 55 (2002), no. 12, 1569–1639.
• T. Grava, From the solution of the Tsarev system to the solution of the Whitham equations. Math. Phys. Anal. Geom. 4 (2001), no. 1, 65–96.
• Grava, T. Asymptotic solutions of the Whitham equations. Nonlinear evolution equations and dynamical systems (Kolimbary, 1999). J. Nonlinear Math. Phys. 8 (2001), suppl., 128–132.
• Grava, T. Existence of a global solution of the Whitham equation. (Russian) Teoret. Mat. Fiz. 122 (2000), no. 1, 58--71; translation in Theoret. and Math. Phys. 122 (2000), no. 1, 46–57
• Grava, T. Bifurcation diagram of a one-parameter family of dispersive waves. VI Workshop on Partial Differential Equations, Part I (Rio de Janeiro, 1999). Mat. Contemp. 18 (2000), 137–165.