Publications
P. Baldi, M. Berti, R. Montalto. “A note on KAM theory for quasi-linear and fully nonlinear KdV.” Rend. Lincei Mat. Appl. 24, 437-450, 2013.
P. Baldi , M. Berti, R. Montalto. “KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation.” Math. Annalen, 359, 1-2, 471-536, 2014. arxiv.org/pdf/1211.6672.pdf
P. Baldi , M. Berti, R. Montalto. “KAM for quasi-linear KdV.” C. R. Acad. Sci. Paris, Ser. I 352, 603-607, 2014.
P. Baldi , M. Berti, R. Montalto. “KAM for autonomous quasi-linear perturbations of KdV.” Ann. I. H. Poincarè (C) Anal. Non Linèaire 33, 1589-1638, 2016. https://arxiv.org/pdf/1404.3125.pdf
P. Baldi , M. Berti, R. Montalto. “KAM for autonomous quasi-linear perturbations of mKdV.” Boll. Unione Mat. Ital, 9, 143-188, 2016. arxiv.org/pdf/1508.02007.pdf
M. Berti, T. Kappeler, R. Montalto. “Large KAM tori for perturbations of the dNLS equation.” Asterisque 403. 2018. arxiv.org/pdf/1603.09252.pdf
T. Kappeler, R. Montalto. “Canonical coordinates with tame estimates for the Defocusing NLS Equation on the Circle.” Int. Math. Res. Notices 2018(5), pp. 1473-1531, doi: 10.1093/imrn/rnw233, 2016. arxiv.org/pdf/1607.04454.pdf
M. Berti, R. Montalto. “Quasi-periodic water waves.” J. Fixed Point Theory Appl., 19(1), 129-156, 2017.
R. Montalto. “Quasi-periodic solutions of forced Kirchhoff equation.” Nonlinear Differ. Equ. Appl. NoDEA, 24(1), 9, 2017. arxiv.org/pdf/1602.05093.pdf
R. Montalto. “A reducibility result for a class of linear wave equations on T^d.” Int. Math. Res. Notices, doi: 10.1093/imrn/rnx167, 2017. arxiv.org/pdf/1702.06880.pdf
P. Baldi, E. Haus, R. Montalto. “Controllability of quasi-linear Hamiltonian NLS equations.” Journal of Differential Equations, 264(3), pp. 1786-1840, 2018. https://doi.org/10.1016/j.jde.2017.10.009. arxiv.org/pdf/1610.09196.pdf
R. Montalto. “On the growth of Sobolev norms for a class of linear Schrödinger equations on the torus with superlinear dispersion.” Asymptotic Analysis, 108(1-2), pp. 85-114, 2018. arxiv.org/pdf/1706.09704.pdf
P. Baldi, M. Berti, E. Haus, R. Montalto. “Time quasi-periodic gravity water waves in finite depth.” Inventiones Math. 214 (2), 739-911, (DOI:10.1007/s00222-018-0812-2), 2018. arxiv.org/pdf/1708.01517.pdf
P. Baldi, M. Berti, E. Haus, R. Montalto. “KAM for gravity water waves in finite depth.” Rend. Lincei Mat. Appl., 29(2), pp. 215-236, 2018.
R. Montalto. "Growth of Sobolev norms for time dependent periodic Schrödinger equations with sublinear dispersion." Journal of Differential Equations 266(8), pp. 4953-4996, https://doi.org/10.1016/j.jde.2018.10.017. 2018. arxiv.org/pdf/1802.04138.pdf
R. Feola, F. Giuliani, R. Montalto, M. Procesi. "Reducibility of first order linear operators on tori via Moser's theorem." Journal of Functional Analysis, 276 (2019) 932–970, DOI:10.1016/j.jfa.2018.10.009. arxiv.org/pdf/1801.04224.pdf
L. Corsi, R. Montalto. "Quasi-periodic solutions for the forced Kirchhoff equation on T^d." Nonlinearity 31,5075-5109 (https://doi.org/10.1088/1361-6544/aad6fe), 2018. arxiv.org/pdf/1802.04139.pdf
D. Bambusi, R. Montalto. "Reducibility of 1-d Schrodinger equation with unbounded time quasi-periodic perturbations." III. Journal of Mathematical Physics 59, 122702 (2018); DOI: 10.1063/1.5048726. arxiv.org/pdf/1807.06328.pdf
D. Bambusi, B. Langella, R. Montalto. "Reducibility of non-resonant transport equation on T^d with unbounded perturbations." Annales Henri Poincaré, 20 (2019) 1893-1929. arxiv.org/pdf/1808.01504.pdf
T. Kappeler, R. Montalto. "Normal form coordinates for the KdV equation having expansions in terms of pseudo differential operators." Communications in Math. Physics, 375(1), 2020, pp. 833-913 arxiv.org/pdf/1812.05391.pdf
M. Bert, R. Montalto. "Quasi-periodi standing wave solutions of gravity-capillary Water Waves." Memoirs of the American Mathematical Society, 263(1273), pp. 1-184 (2020).
D. Bambusi, B. Langella, R. Montalto. "On the spectrum of the Schrödinger operator on T^d: a normal form approach.". Communications in PDEs, 45(4), 2020 pp. 303-320, arxiv.org/pdf/1903.09449.pdf
L. Corsi, R. Montalto, M. Procesi. "Almost-periodic Response Solutions for a forced quasi-linear Airy equation." Journal of Dynamics and Dierential Equations, https://doi.org/10.1007/s10884-020-09906-8 (2020) https://arxiv.org/pdf/2006.00313.pdf
M. Berti, T. Kappeler, R. Montalto. "Large KAM tori for quasi-linear perturbations of KdV ." Archive for Rational Mechanics and Analysis (ARMA), 239 (2021) 1395-1500.https://doi.org/10.1007/s00205-020-01596, arxiv.org/abs/1908.08768
R. Montalto, M. Procesi. "Linear Schrodinger equation with an almost periodic potential." SIAM Journal of Mathematical Analysis. Vol. 53, No. 1, pp. 386-434 (2021).https://doi.org/10.1137/20M1320742. arxiv.org/abs/1910.12300
R. Montalto. " The Navier-Stokes equation with time quasi-periodic external force: existence and stability of quasi-periodic solutions" Journal of Dynamics and Differential Equations. https://doi.org/10.1007/s10884-021-09944-w (2021) arxiv.org/pdf/2005.13354.pdf
P. Baldi, R. Montalto. "Quasi periodic incompressible Euler flows in 3D." Advances in Mathematics 384 (2021) 107730. https://doi.org/10.1016/j.aim.2021.107730. arxiv.org/pdf/2003.14313.pdf
T. Kappeler, R. Montalto. "On the stability of periodic multi-solitons of the KdV equation." Communications in Mathematical Physics. 385, 1871-1956 (2021). https://doi.org/10.1007/s00220-021-04089-9 arxiv.org/pdf/2009.02721.pdf
D. Bambusi, B. Langella, R. Montalto. " Spectral asymptotics of all the eigenvalues of Schrodinger operators on flat tori." Nonlinear Analysis, Theory, Methods and Applications, 2022, 216, 112679. arxiv.org/pdf/2007.07865.pdf
D. Bambusi, B. Langella, R. Montalto. "Growth of Sobolev norms for unbounded perturbations of the Laplacian on flat tori." Journal of Differential Equations, 2022, 318, pp. 344-358. arxiv.org/pdf/2012.02654.pdf
R. Feola, R. Montalto. "Quadratic lifespan and growth of Sobolev norms for derivative Schrodinger equations on generic tori." Journal of Differential Equations, 2022, 312, pp. 276-316. arxiv.org/pdf/2103.10162.pdf
D. Bambusi, R. Feola, R. Montalto. "Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori." Preprint arXiv:2208.00413 (2022). arxiv.org/pdf/2208.00413.pdf
T. Kappeler, R. Montalto."Normal form coordinates for the Benjamin-Ono equation having expansions in terms of Pseudo-differential operators." Discrete and Continuous Dynamical Systems series A, 42(9), pp. 4127–4201 (2022). arxiv.org/pdf/2109.02489.pdf
L. Franzoi, R. Montalto. "A KAM approach to the inviscid limit for the 2D Navier-Stokes equations." Preprint arXiv:2207.11008 (2022) arxiv.org/pdf/2207.11008.pdf
L. Franzoi, N. Masmoudi, R. Montalto. "Space quasi-periodic steady Euler flows close to the inviscid Couette flow" Preprint arxiv.org/pdf/2303.03302.pdf (2023)