Tamara Grava

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Integrability and randomness

  1. Integrable systems with random initial data and random Lax matrices
  2. Probabilistic Riemann-Hilbert problems
  3. Solitons, interacting particles and generalised hydrodynamics
I study integrable nonlinear dispersive equations and discrete equations with random initial data deriving typical behaviours and fluctuation of their solutions (3. 7. 8. 9. 10.) In particular I am studying soliton gases that are a collection of solitons with random parameters that interact elastically with each other, similar to a gas of particles (3.). Soliton gases describe a wide range of strongly nonlinear phenomena in fluids and optical media and are linked to fundamental nonlinear behaviours such as the formation of rogue waves and the modulation instability. In a deterministic setting I have studied the collective behaviour of large set of solitons and derived the generalised hydrodynamic equations for the average description of their interactions (1. 2. 5. 6. 11.)

Relevant publications

  1. Shielding of breathers for the focusing nonlinear Schroedinger equation. G. Falqui, T. Grava, C. Puntini. Preprint.
  2. Dbar-problem for focusing nonlinear Schrödinger equation and soliton shielding. M.Bertola, T. Grava, G. Orsatti. Preprint.
  3. Law of Large Numbers and Central Limit Theorem for random sets of solitons of the focusing nonlinear Schrödinger equation. M. Girotti, T. Grava, K.D. T-R McLaughlin, J. Najnudel, Preprint.
  4. Integrable operators, dbar-problems, KP and NLS hierarchy. M.Bertola, T. Grava, G. Orsatti. Nonlinearity 37 (2024), no. 8, Paper No. 085008, 33 pp.
  5. Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation. Girotti, Manuela; Grava, Tamara; Jenkins, Robert; McLaughlin, Ken T.-R.; Minakov, Alexander Comm. Pure Appl. Math. 76 (2023), no. 11, 3233-3299.
  6. Soliton shielding of the focusing nonlinear Schrödinger equation. Bertola, Marco; Grava, Tamara; Orsatti, Giuseppe Phys. Rev. Lett. 130 (2023), no. 12, Paper No. 127201, 6 pp.
  7. Equilibrium spacetime correlations of the Toda lattice on the hydrodynamic scale. Mazzuca, Guido; Grava, Tamara; Kriecherbauer, Thomas; McLaughlin, Kenneth T.-R.; Mendl, Christian B.; Spohn, Herbert J. Stat. Phys. 190 (2023), no. 8, Paper No. 149, 22 pp.
  8. Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular β -ensemble and double confluent Heun equation. Grava, Tamara; Mazzuca, Guido Comm. Math. Phys. 399 (2023), no. 3, 1689-1729.
  9. Discrete integrable systems and random Lax matrices. Grava, Tamara; Gisonni, Massimo; Gubbiotti, Giorgio; Mazzuca, Guido J. Stat. Phys. 190 (2023), no. 1, Paper No. 10, 35 pp.
  10. Correlation functions for a chain of short range oscillators. Grava, T.; Kriecherbauer, T.; Mazzuca, G.; McLaughlin, K. D. T.-R. J. Stat. Phys. 183 (2021), no. 1, Paper No. 1, 31 pp.
  11. Rigorous asymptotics of a KdV soliton gas. Girotti, M.; Grava, T.; Jenkins, R.; McLaughlin, K. D. T.-R. Comm. Math. Phys. 384 (2021), no. 2, 733–784.
  12. Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit. Grava, T.; Maspero, A.; Mazzuca, G.; Ponno, A. Comm. Math. Phys. 380 (2020), no. 2, 811–851.