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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Istituto Nazionale di Fisica Nucleare, Sezione di LecceIT2.1k papers
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- Sapienza University of RomeIT1.3k papers
- Istituto Nazionale di Fisica Nucleare, Sezione di MilanoIT1.3k papers
- University of BolognaIT1.3k papers
- University of MilanIT1.3k papers
- Institut National de Physique Nucléaire et de Physique des ParticulesFR1.3k papers
- University of GenevaCH1.3k papers
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62 papers · 1 filter
Compatible pairs of Hamiltonian operators of the first and third orders
Paolo Lorenzoni, Stanislav Opanasenko, Raffaele Vitolo
We compute general compatibility conditions between a weakly nonlocal homogeneous Hamiltonian operator and a third-order homogeneous Hamiltonian operator. Such operators determine…
Bi-Hamiltonian structures of WDVV-type
S. Opanasenko, R. Vitolo
We study a class of nonlinear PDEs that admit the same bi-Hamiltonian structure as WDVV equations: a Ferapontov-type first-order Hamiltonian operator and a homogeneous third-order…
On solutions to a novel non-evolutionary integrable 1+1 PDE
Francesco Giglio, Giulio Landolfi, Luigi Martina
We investigate real solutions of a C-integrable non-evolutionary partial differential equation in the form of a scalar conservation law where the flux density depends both on the d…
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom
Giovanni De Matteis, Francesco Giglio, Antonio Moro
We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition functi…
On universality of homogeneous Euler equation
B. G. Konopelchenko, G. Ortenzi
Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions pr…
Self-dual Einstein spaces and the general heavenly equation. Eigenfunctions as coordinates
B. G. Konopelchenko, W. K. Schief, A. Szereszewski
Eigenfunctions are shown to constitute privileged coordinates of self-dual Einstein spaces with the underlying governing equation being revealed as the general heavenly equation. T…
On an integrable multi-dimensionally consistent 2n+2n-dimensional heavenly-type equation
B. G. Konopelchenko, W. K. Schief
Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2n+2n-dimensional integrable partial…
Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
Decio Levi, Luigi Martina, Pavel Winternitz
The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra with the simple Lie algebra as its maximal finite-dimensional subalgeb…
Systems of conservation laws with third-order Hamiltonian structures
E. V. Ferapontov, M. V. Pavlov, R. F. Vitolo
We investigate -component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is redu…
KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices
M. Boiti, F. Pempinelli, A. K. Pogrebkov
Direct definition of the Cauchy-Jost (known also as Cauchy-Baker-Akhiezer) function in the case of pure solitonic solution is given and properties of this function are discussed in…
The three-component defocusing nonlinear Schrodinger equation with nonzero boundary conditions
Gino Biondini, Daniel Kraus, Barbara Prinari
We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrodinger (NLS) equation with initial conditions approaching c…
Confluence of hypergeometric functions and integrable hydrodynamic type systems
Y. Kodama, B. Konopelchenko
It is known that a large class of integrable hydrodynamic type systems can be constructed through the Lauricella function, a generalization of the classical Gauss hypergeometric fu…
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests
Decio Levi, Luigi Martina, Pavel Winternitz
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Thre…
Integrable discretization of hodograph-type systems, hyperelliptic integrals and Whitham equations
B. G. Konopelchenko, W. K. Schief
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the…
Critical points, Lauricella functions and Whitham-type equations
Y. Kodama, B. Konopelchenko, W. K. Schief
A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darbo…
Projective-geometric aspects of homogeneous third-order Hamiltonian operators
Eugene V. Ferapontov, Maxim V. Pavlov, Raffaele F. Vitolo
We investigate homogeneous third-order Hamiltonian operators of differential-geometric type. Based on the correspondence with quadratic line complexes, a complete list of such oper…
Linearly Degenerate Hamiltonian PDEs and a New Class of Solutions to the WDVV Associativity Equations
B. A. Dubrovin, M. V. Pavlov, S. A. Zykov
We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution…
Projective differential geometry of multidimensional dispersionless integrable hierarchies
L. V. Bogdanov, B. G. Konopelchenko
We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential -form with the coefficients satisfying the Plücker relatio…
Waves in the Skyrme--Faddeev model and integrable reductions
L. Martina, M. V. Pavlov, S. A. Zykov
In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging metho…
Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems
L. V. Bogdanov, B. G. Konopelchenko
Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms of rank N-1 naturally associated with Gr(N-1,…
Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter
B. G. Konopelchenko, G. Ortenzi
Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic syst…
Extended resolvent of heat operator with multisoliton potential
M. Boiti, F. Pempinelli, A. K. Pogrebkov
The heat operator with a general multisoliton potential is considered and its extended resolvent, depending on a parameter is derived. Its boundedness properties in all…
Green's function of heat operator with pure soliton potential
M. Boiti, F. Pempinelli, A. K. Pogrebkov
The heat operator with a pure soliton potential is considered and its Green's function, depending on a complex spectral parameter k, is derived. Its boundedness properties in all v…
A unified approach to computation of integrable structures
Iosif Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of par…