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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University of SalentoIT2.1k papers
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- Centre National de la Recherche ScientifiqueFR1.3k papers
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- Sapienza University of RomeIT1.2k papers
- Istituto Nazionale di Fisica Nucleare, Sezione di BolognaIT1.2k papers
- Institut National de Physique Nucléaire et de Physique des ParticulesFR1.2k papers
- University of BolognaIT1.2k papers
- University of GenevaCH1.2k papers
- University of MilanIT1.2k papers
- National Institute for Subatomic PhysicsNL1.2k papers
63 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…
On an integrable 2+1-dimensional extended Dym equation: Lax pair, -dressing scheme and modulation
Boris Konopelchenko, Colin Rogers, Pablo Amster
In 1+1-dimensions, an extension of the canonical solitonic Dym equation has previously been derived both in a geometric torsion evolution context and in the analysis of peakon soli…
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…
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…
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…
Integrability properties of symmetric 4+4-dimensional heavenly type equation
L. V. Bogdanov, B. G. Konopelchenko
We demonstrate that the dispersionless -dressing method developed before for general heavenly equation is applicable to the and - dimensional symmetric…
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…
Integrable extended van der Waals model
Francesco Giglio, Giulio Landolfi, Antonio Moro
Inspired by the recent developments in the study of the thermodynamics of van der Waals fluids via the theory of nonlinear conservation laws and the description of phase transition…
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 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,…
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…
Gradient catastrophe and flutter in vortex filament dynamics
B. G. Konopelchenko, G. Ortenzi
Gradient catastrophe and flutter instability in the motion of vortex filament within the localized induction approximation are analyzed. It is shown that the origin if this phenome…
Heat operator with pure soliton potential: properties of Jost and dual Jost solutions
M. Boiti, F. Pempinelli, A. Pogrebkov
Properties of Jost and dual Jost solutions of the heat equation, and , in the case of a pure solitonic potential are studied in detail. We describe their analytica…
On the singular sector of the Hermitian random matrix model in the large N limit
B. Konopelchenko, L. Martinez Alonso, E. Medina
The singular sector of zero genus case for the Hermitian random matrix model in the large N limit is analyzed. It is proved that the singular sector of the hodograph solutions for…
Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation
B. Konopelchenko, L. Martinez Alonso, E. Medina
It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the…
On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
Marco Boiti, Flora Pempinelli, Andrei K. Pogrebkov +1
The unexpectedly rich structure of the multisoliton solutions of the KPII equation has been explored by using different approaches, running from dressing method to twisting transfo…