2014

A.Belavin, B.Dubrovin, B.Mukhametzhanov, Minimal Liouville gravity correlation numbers from Douglas string equation. Journal of High Energy Physics, January 2014, 2014:156, pp. 1-50

M.Bertola, M.Gekhtman, J.Szmigielski, Cauchy - Laguerre two-matrix model and the Meijer-G random point field, Commun. Math. Phys., Vol. 326 (2014) 111-144

A.Brini, G.Carlet, S.Romano, P.Rossi, Rational reductions of the 2D-Toda hierarchy and mirror symmetry. arXiv:1401.5725

A.De Sole, V.Kac, D.Valeri, Adler - Gelfand - Dickey approach to classical W-algebras within the theory of Poisson vertex algebras. arXiv:1401.2082

A. De Sole, V.Kac, D.Valeri, Integrability of Dirac reduced bi-Hamiltonian equations. arXiv:1401.6006

B.Dubrovin, Gromov - Witten invariants and integrable hierarchies of topological type. arXiv:1312.0799, to appear in Amer. Math. Soc. Transl, 2014

B.Dubrovin, A.Kapaev, On an isomonodromy deformation equation without the Painlevé property. arXiv:1301.7211, to appear in Russ. J. Math. Phys., Vol. 21, no. 1 (2014)

B.Dubrovin, Si-Qi Liu, Di Yang, Youjin Zhang, Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs, to appear

A. Figalli, C. Klein, P. Markowich and C. Sparber, WKB analysis of Bohmian dynamics. Comm. Pure Appl. Math., Vol. 67 (2014) 581-620

R.Jenkins, Regularization of a sharp shock by the defocusing nonlinear Schrödinger equation. arXiv:1402.4708

D.Masoero, A.Raimondo, Semiclassical limit for generalized KdV equations before the gradient catastrophe. Constr. Approx., Vol. 39 (2014) 43-74

A.Moro, Shock dynamics of phase diagrams. Annals of Physics, Vol. 343 (2014) 49-60

A.Moro, S.Trillo, Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation. Phys. Rev. E 89 (2014) 023202

Chao-Zhong Wu, Dafeng Zuo, Infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, Adv. Math., Vol. 255 (2014) 487-524

A.Arsie, P.Lorenzoni, A.Moro, Integrable viscous conservation laws. arXiv:1301.0950

J.Baik, R.Jenkins, Limiting distribution of maximal crossing and nesting of Poissonized random matchings. Ann. Probab., Vol. 41 (2013) 4359-4406

F.Balogh, D.Merzi, Equilibrium measures for a class of potentials with discrete rotational symmetry, arXiv:1312.1483

M.Bertola, M.Cafasso, The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation. Random Matrices: Theory and Applications, Vol. 2 (2013) 1350003, 18 pp.

M.Bertola, A.Katsevich, A.Tovbis, Inversion formulae for the cosh-weighted Hilbert transform. Proceedings Amer. Math. Soc., Vol. 141 (2013) 2703-2718

M.Bertola, A.Tovbis, Universality for the focusing nonlinear Schroedinger equation at the gradient catastrophe point: rational breathers and poles of the tritronquee solution to Painlevé-I. Studies Appl. Math., Vol. 66 (2013) 678-752

M.Casati, On deformations of multidimensional Poisson brackets of hydrodynamic type, arXiv:1312.1878

T.Claeys, S.Romano, Biorthogonal ensembles with two-particle interactions, arXiv:1312.2892

T.Claeys, F.Wielonsky, On sequences of rational interpolants of the exponential function with unbounded interpolation points. J. Approx. Theory 171 (2013), 1-32.

A.De Sole, V.Kac, D.Valeri, Classical W-algebras and generalized Drinfeld - Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Commun. Math. Phys., Vol. 323 (2013) 663-711

Y.Dinar, Frobenius manifolds from subregular classical W-algebras, IMRN 2013, no. 12, 2822-2861

B.Dubrovin, T.Grava, C.Klein, A.Moro, On critical behavior in systems of Hamiltonian partial differential equations, arXiv:1311.7166

E.Ferapontov, V.Novikov, I.Roustemoglou, Towards the classification of integrable differential-difference equations in 2+1 dimensions. J. Phys. A 46 (2013), no. 24, 245207

P. Giavedoni, Period matrices of real Riemann surfaces and fundamental domains, SIGMA, Vol. 9 (2013) 062, 25 pages

A.Kapaev, C.Klein, T.Grava, On the tritronquée solutions of P_I^2. arXiv:1306.6161

C.Klein, B.Muite, K.Roidot, Numerical study of blow-up in the Davey-Stewartson system. Discrete Contin. Dyn. Syst. Ser. B 18 (2013), no. 5, 1361-1387.

C.Klein, K.Roidot, Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations. Phys. D 265 (2013), 1-25.

Si-Qi Liu, Di Yang, Youjin Zhang, Uniqueness theorem of W-constraints for simple singularities. Lett. Math. Phys., Vol. 103 (2013) 1329-1345

Si-Qi Liu, Youjin Zhang, Bihamiltonian cohomologies and integrable hierarchies I: a special case. Commun. Math. Phys., Vol. 324 (2013) 897-935

D.Masoero, A.Raimondo, A deformation of the method of characteristics and the Cauchy problem for Hamiltonian PDEs in the small dispersion limit. IMRN 2013, no. 11, 1-39

D.Masoero, A.Raimondo, P.Antunes, Critical behaviour for scalar nonlinear waves. arXiv:1312.3880

Chao-Zhong Wu, From additional symmetries to linearization of Virasoro symmetries, Physica D, Vol. 249 (2013) 25-37

Chao-Zhong Wu, R-matrices and Hamiltonian structures for certain Lax equations. Rev. Math. Phys., Vol. 25 (2013) 1350005, 27 pp.

2012

A.Brini, Open topological strings and integrable hierarchies: remodelling the A-model. Commun. Math. Phys., Vol. 312 (2012) 735-780.

A.Brini, The local Gromov - Witten theory of CP^1 and integrable hierarchies. Commun. Math. Phys., Vol. 313 (2012) 571-605

A.Brini, G.Carlet, P.Rossi, Integrable hierarchies and the mirror model of local CP^1. Phys. D 241 (2012), no. 23-24, 2156-2167.

Claeys T. The Riemann-Hilbert approach to obtain critical asymptotics for Hamiltonian perturbations of hyperbolic and elliptic systems Random Matrices: Theory and Applications (2012), accepted for publication. Click here for PDF

Claeys T. Pole-free solutions of the first Painlevé hierarchy and non-generic critical behaviour for the KdV equation, Physica D (2012), accepted for publication. Click here for PDF

T.Claeys, T.Grava, The KdV hierarchy: universality and a Painlevé transcendent. IMRN 2012, no. 22, 5063-5099.

T.Claeys, Dong Wang, Random matrices with equispaced external source, arXiv:1212.3768, to appear in Comm. Math. Phys.

G. De Nittis, A.Moro, Thermodynamic phase transitions and shock singularities. Proc. R. Soc. Lond. Ser A Math. Phys. Eng. Sci., Vol. 468 (2012) 701-719

B.Dubrovin, M.Elaeva, On the critical behavior in nonlinear evolutionary PDEs with small viscosity. Russ. J. Math. Phys. 19 (2012), no. 4, 449-460.

B.Dubrovin, S.-Q.Liu, Y.Zhang, On the genus two free energies for semisimple Frobenius manifolds. Russ. J. Math. Phys. 19 (2012), no. 3, 273-298.

B.Dubrovin, T.Skrypnyk, Classical double, R-operators, and negative flows of integrable hierarchies. Theor. Math. Phys., Vol. 172 (2012) 911-931

E.Ferapontov, B.Huard, A.Zhang, On the central quadric ansatz: integrable models and Painlevé reductions. J. Phys. A 45 (2012), no. 19, 195204

E.Ferapontov, B.Kruglikov, Dispersionless integrable systems in 3D and Einstein - Weyl geometry, arXiv:1208.2728

E.Ferapontov, V.Novikov, N.Stoilov, Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions. Phys. D 241 (2012), no. 23-24, 2138-2144.

S.Garoufalidis, A.Its, A.Kapaev, M.Mariño, Asymptotics of the instantons of Painlevé -I, IMRN 2012, no. 3, 561-606

T.Grava, 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.

C.Kalla, C.Klein, On the numerical evaluation of algebro-geometric solutions to integrable equations. Nonlinearity 25 (2012), no. 3, 569-596.

C.Kalla, C.Klein, New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 468 (2012), no. 2141, 1371-1390.

C.Klein, J.-C.Saut, Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations. J. Nonlinear Sci. 22 (2012), no. 5, 763-811.

Si-Qi Liu, Dingdian Xu, Youjin Zhang, The inversion symmetry of the WDVV equations and tau-functions, Phys. D., Vol. 241 (2012) 2168-2177

E.Parodi, On classification of discrete, scalar-valued Poisson brackets. J. Geom. Phys., Vol. 62 (2012) 2059-2076

A.Raimondo, Frobenius manifolds for the dispersionless Kadomtsev - Petviashvili equation. Commun. Math. Phys., Vol. 311 (2012) 557-594

Chao-Zhong Wu, Tau-functions and Virasoro symmetries for Drinfeld - Sokolov hierarchies, arXiv:1203.5750

Chao-Zhong Wu, Dingdian Xu, A class of infinite-dimensional Frobenius manifolds and their submanifolds, IMRN, Vol. 2012, no.19, 4520-4562

2011

M.Bertola, M.Cafasso, The Riemann - Hilbert approach to the transition between the gap probabilities from the Pearcey to the Airy process, IMRN, Vol. 2012 (2011) 1519-1568.

Carlet G., Dubrovin B., Mertens L.P. Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems, Math. Annalen 349 (2011), 75--115. Click here for PDF

Carlet G., Mertens L.P., Principal hierarchies of infinite-dimensional Frobenius manifolds: the extended 2D Toda lattice, arXiv:1109.5343

Claeys T., A.Its, I.Krasovsky, Emergence of a singularity for Toeplitz determinants and Painlevé V. Duke Math. J. 160 (2011), no. 2, 207-262. Click here for PDF

Dinar Y. Frobenius manifolds from regular classical W-algebras, Advances Math. 226 (2011), 5018--5040. Click here for PDF

Dubrovin B., Grava T. and Klein C. Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations. J. of Nonlinear Science 19 (2009), 57-94. Click here for PDF

Dubrovin B., Pavlov M., Zykov S. Linearly-degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations, Functional Analysis and Appl. 45 No. 4 (2011 accepted for publication). Click here for PDF

Ferapontov E.V., Khusnutdinova K.R., Klein C. On linear degeneracy of integrable quasilinear systems in higher dimensions, Lett. Math. Phys. 96 (2011), 5--35. Click here for PDF

Ferapontov E.V., Odesskii A.V. and Stoilov, N.M. Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions, J. Math. Physics 52 (2011) 073505. Click here for PDF

Frauendiener J., Klein C., Shramchenko V. Efficient computation of the branching structure of an algebraic curve, Comput. Methods Funct. Theory 11 (2011), 527-546. Click here for PDF

M.Grenier, H.-R.Jauslin, C.Klein, V.Matveev, Wave attraction in resonant counter-propagating wave systems. J. Math. Phys. 52 (2011), no. 8, 082704, 15 pp.

R.Jenkins, K.McLaughlin, The semiclassical limit of focusing NLS for a family of non-analytic initial data. arXiv:1106.1699

Kalla C. Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions, J. Phys. A: Math. Theor. 44 (2011) 335210. Click here for PDF

Klein C., Roidot K. Fourth order time-stepping for Kadomtsev-Petviashvili and Davey-Stewartson equations, SIAM J. Sci. Computation. 33 (2011) no. 6, 3333-3356 Click here for PDF

Si-Qi Liu, Youjin Zhang, Jacobi structures of evolutionary partial differential equations, Advances Math. 227 (2011), 73--130. Click here for PDF

Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang, On the Drinfeld-Sokolov hierarchies of D type, International Math. Research Notices 2011 (2011), 1952--1996. Click here for PDF

P.Lorenzoni, M.Pedroni, A.Raimondo, F-manifolds and integrable systems of hydrodynamic type. Arch. Math. (Brno), Vol. 47 (2011) 163-180

Moro A. and De Nittis G. Thermodynamic phase transitions and shock singularities, Proc. Royal Soc., Ser. A, (2011, accepted for publication). Click here for PDF

Novikov V.S., Ferapontov E.V. On the classification of scalar evolutionary integrable equations in 2+1 dimensions, J. Math. Phys. 52 (2011), 023516. Click here for PDF

Chao-Zhong Wu, Dingdian Xu, A class of infinite-dimensional Frobenius manifolds and their submanifolds, International Math. Research Notices (2011, published online 19.10.2011). Click here for PDF

2010

M.Bertola, The dependence on the monodromy data of the isomonodromic tau function, Commun. Math. Phys., Vol. 294 (2010) 539-579

Bertola M. and Lee S.Y. First colonization of a hard-edge in random matrix theory, Constructive Approximation 31 (2010) 231--257. Click here for PDF

Burovskiy P.A., Ferapontov E.V. Tsarev S.P. Second order quasilinear PDEs and conformal structures in projective space, International J. Math. 21 (2010) 799--841. Click here for PDF

Dubrovin B. and Skrypnyk T. Classical double, R-operators and negative flows of integrable hierarchies. Preprint: arXiv:1011.4894[nlin.SI] (2010). Click here for PDF

Claeys T. Asymptotics for a special solution to the second member of the Painleve I hierarchy. J. Phys. A 43 (2010), no. 43, 434012, 18 pp. Click here for PDF

Claeys T. Higher order analogues of the Tracy-Widom distribution and the Painleve II hierarchy. (With Its, A. and Krasovsky, I.). Comm. Pure Appl. Math. 63 (2010), no. 3, 362--412. Click here for PDF

Claeys T. and Grava T. Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit. Comm. Pure Appl. Math. 63 (2010), no. 2, 203--232. Click here for PDF

Claeys T. and Grava T. Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit. SIAM J. Math. Anal. 42 (2010), no. 5, 2132--2154. Click here for PDF

Doubrov B. and Ferapontov E.V. On the integrability of symplectic Monge – Ampère equations, J. Geom. Phys. 60 (2010), 1604--1616. Click here for PDF

Dubrovin B. Hamiltonian PDEs: deformations, integrability, solutions, J. of Physics A: Math. And Theor. 43 (2010), 434002-434022. Click here for PDF

Ferapontov E.V. and Odesskii A.V. Integrable Lagrangians and modular forms. J. Geom. Phys. 60 (2010), no. 6-8, 896--906. Click here for PDF

Ferapontov E.V. Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian. (With Hadjikos, L. and Khusnutdinova, K. R.). Int. Math. Res. Not. IMRN (2010), no. 3, 496--535. Click here for PDF

Grava T. and Klein C. Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions. (With Abenda, S.). SIAM J. Appl. Math. 70 (2010), no. 8, pp. 2797--2821. Click here for PDF .

Masoero D. Poles of intègrale tritronquée and anharmonic oscillators. A WKB approach, J. Phys. A: Math. Theor. 43 (2010) 095201. Click here for PDF .

Masoero D. Poles of intègrale tritronquée and anharmonic oscillators. Asymptotic localization from WKB analysis, Nonlinearity 23 (2010), 2501. Click here for PDF .

Masoero D. Y-system and deformed thermodynamic Bethe ansatz, Lett. Math. Phys. 94 (2010) 151-164. Click here for PDF .

D.Masoero, A simple algorithm for computing Stokes multipliers, arXiv:1007.1554

Chao-Zhong Wu, Dingdian Xu, Bihamiltonian structure of the two-component Kadomtsev - Petviashvili hierarchy of type B, J. Math. Phys. 51 (2010) 063504

2009

Abriani D., Frobenius manifolds associated to Coxeter groups of type E7 and E8, arXiv:0910.5453

Bertola M. Moment determinants as isomonodromic tau functions, Nonlinearity 22 (2009), 29--50. Click here for PDF

Bertola M., Gekhtman, M., Szmiegielski J. The Cauchy two-matrix model, Commun. Math. Phys. 287 (2009), 983--1014. Click here for PDF

Bertola M. and Lee S. Y. First colonization of a spectral outpost in random matrix theory, Constructive Approximation 30 (2009), 225--263. Click here for PDF

Bertola M. and Marchal O. The partition function of the two-matrix model as an isomonodromic tau-function, J. Math. Phys. 50 (2009) 013529. Click here for PDF

Bertola M., A. Prats Ferrer, Topological expansion for the Cauchy two-matrix model, J. Phys. A 42 (2009) 335201

Bertola M., Mo M.Y. Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights, Advances in Math. 220 (2009) 154--218. Click here for PDF

Bertola M., S.Y.Lee, First colonization of a spectral outpost in random matrix theory. Constructive Approximation, Vol. 30 (2009) 225-263

Bertola M., M.Gekhtman, J.Szmigielski, Cauchy biorthogonal polynomials, arXiv:0904.2602

Bertola M., S.Y.Lee, M.Y.Mo, Mesoscopic colonization of a spectral band, J. Phys. A: Math. Theor., Vol. 42 (2009) 415204

Ming Chen, Si-Qi Liu, Youjin Zhang, Hamiltonian structures and their reciprocal transformations for the r-KdV-CH hierarchy, J. Geom. and Phys. 59 (2009) 1227-1243

Dubrovin B., Grava T. and Klein C. On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the tritronquée solution to the Painlevé-I equation. J. Nonlinear Sci. 19 (2009), no. 1, 57--94. Click here for PDF

Dinar Y., Remarks on bihamiltonian geometry and classical W-algebras, arXiv:0911.2116

Claeys T. and Grava T. 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. Click here for PDF

Ferapontov E.V., Moro A., Novikov V.S. Integrable systems in 2+1 dimensions: deformations of dispersionless limits. J. Phys. A 42 (2009), no. 34, 345205, 18 pp. Click here for PDF

Ferapontov E.V. and Moro A. Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems. J. Phys. A 42 (2009), no. 3, 035211, 15 pp. Click here for PDF

Ferapontov E.V., Moro A., Sokolov V.V. Hamiltonian systems of hydrodynamic type in 2+1 dimensions. Comm. Math. Phys. 285 (2009), no. 1, 31--65. Click here for PDF

Grava T. Initial value problem of the Whitham equations for the Camassa-Holm equation. (With Pierce, V. U. and Tian, Fei-Ran). Physica D 238, (2009), no. 1, 55--66. Click here for PDF

Klein C. Extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of genus two Riemann surfaces. (With Kokotov, A. and Korotkin, D.). Math. Z. 261 (2009), no. 1, 73--108. Click here for PDF

A. Moro, Hodographic vortices. Phys. Lett. A 373 (2009) 3021-3023

Chao-Zhong Wu, A remark on Kac - Wakimoto hierarchies of D-type, arXiv:0906.5360

Books: Monographs and Edited Volumes

Bobenko A. and Klein C. (eds.) Computational Approach to Riemann Surfaces, Lecture Notes in Mathematics vol. 2013, Springer Verlag, 257 pages (2011).

Book Chapters

T.Claeys, S.Olver, Numerical study of higher order analogues of the Tracy-Widom distribution. Recent advances in orthogonal polynomials, special functions, and their applications, 83-98, Contemp. Math., 578, Amer. Math. Soc., Providence, RI, 2012.

Dubrovin B. Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions, In New Trends in Mathematical Physics. Selected contributions of the XVth International Congress on Mathematical Physics, Sidoravicius Vladas (ed.), Springer Verlag (2009) p. 231-276. Click here for PDF

Frauendiener J., Klein C. Algebraic curves and Riemann surfaces in Matlab, In Computational Approach to Riemann Surfaces, Bobenko A. and Klein C. (eds.) Springer Lecture Notes in Mathematics vol. 2013 (2011), 125-162. Click here for PDF

C.Klein, C.Sparber, Transverse stability of periodic traveling waves in Kadomtsev-Petviashvili equations: a numerical study. Recent advances in harmonic analysis and partial differential equations, 155-168, Contemp. Math., 581, Amer. Math. Soc., Providence, RI, 2012.