Dispersive deformations of hydrodynamic reductions of (2 + 1)D dispersionless integrable systems
- E. Ferapontov, A. Moro
- Physics
- 15 July 2008
We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2 + 1 dimensions, such as the dispersionless Kadomtsev–Petviashvili (dKP) and dispersionless Toda lattice (dTl)…
Integrable Equations in Nonlinear Geometrical Optics
- B. Konopelchenko, A. Moro
- Physics
- 29 March 2004
Geometrical optics limit of the Maxwell equations for nonlinear media with the Cole–Cole dependence of dielectric function and magnetic permeability on the frequency is considered. It is shown that…
Hamiltonian Systems of Hydrodynamic Type in 2 + 1 Dimensions
- E. Ferapontov, A. Moro, V. Sokolov
- Physics, Mathematics
- 10 October 2007
We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained.…
Symmetry constraints for real dispersionless Veselov-Novikov equation
- L. V. Bogdanov, B. Konopelchenko, A. Moro
- Physics, Geology
- 14 June 2004
Symmetry constraints for dispersionless integrable equations are discussed. It is shown that under symmetry constraints, the dispersionless Veselov-Novikov equation is reduced to the…
On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations
- B. Dubrovin, T. Grava, C. Klein, A. Moro
- MathematicsJournal of nonlinear science
- 27 November 2013
It is argued that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P$$_I$$I) equation or its fourth-order analogue P$$-I^2$$I2.
Integrable equations in 2 + 1 dimensions: deformations of dispersionless limits
- E. Ferapontov, A. Moro, V. Novikov
- Mathematics
- 20 March 2009
We classify integrable third-order equations in 2 + 1 dimensions which generalize the examples of Kadomtsev–Petviashvili, Veselov–Novikov and Harry Dym equations. Our approach is based on the…
Integrable viscous conservation laws
- A. Arsie, P. Lorenzoni, A. Moro
- Mathematics
- 5 January 2013
We propose an extension of the Dubrovin–Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few…
Shock dynamics of phase diagrams
- A. Moro
- Physics
- 29 July 2013
LETTER TO THE EDITOR: Geometrical optics in nonlinear media and integrable equations
- B. Konopelchenko, A. Moro
- Physics
- 30 December 2003
In an exposure method, using a first exposure apparatus including a reticle having an exposure pattern, a first pattern is formed on a resist film on a semiconductor substrate. Using a second…
Thermodynamic limit and dispersive regularization in matrix models.
- Costanza Benassi, A. Moro
- PhysicsPhysical Review E
- 27 March 2019
This analysis explains the origin and mechanism leading to the emergence of chaotic behaviors observed in M^{6} matrix models and extends its validity to even nonlinearity of arbitrary order.
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