We consider the WDVV associativity equations in the four dimensional case. These nonlinear equations of third order can be written as a pair of six component commuting two-dimensional non-diagonalizable hydrodynamic type systems. We prove that these systems possess a compatible pair of local homogeneous Hamiltonian structures of Dubrovin--Novikov type (of first and third order, respectively)
none2siThe Oriented Associativity equation plays a fundamental role in the theory of Integrable Sys...
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 sup...
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian st...
Combining an old idea of Olver and Rosenau with the classifica- tion of second and third order homo...
AbstractWe show that all the Antonowicz–Fordy type coupled KdV equations have the same symmetry grou...
Following our approach in Ref 2, I present sufficient conditions so that the reciprocal Hamilonian s...
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one o...
We start from a hyperbolic Dubrovin and Novikov (DN) hydrodynamic-type system of dimension n which p...
We consider hydrodynamic systems which possess a local Hamiltonian structure. To such a system there...
AbstractWe establish a close relationship between hamiltonian systems of hydrodynamic type and hyper...
The aim of this article is to classify pairs of the first-order Hamiltonian operators of Dubrovin-No...
We point out a pair of coupled KdV equations which admits a bi-Hamiltonian structure. © 1990 Società...
We define a new class of solutions to the WDVV associativity equations. This class is selected by th...
The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. ...
Abstract. We prove a simple condition under which the metric corresponding to a diagonalizable semi-...
none2siThe Oriented Associativity equation plays a fundamental role in the theory of Integrable Sys...
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 sup...
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian st...
Combining an old idea of Olver and Rosenau with the classifica- tion of second and third order homo...
AbstractWe show that all the Antonowicz–Fordy type coupled KdV equations have the same symmetry grou...
Following our approach in Ref 2, I present sufficient conditions so that the reciprocal Hamilonian s...
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one o...
We start from a hyperbolic Dubrovin and Novikov (DN) hydrodynamic-type system of dimension n which p...
We consider hydrodynamic systems which possess a local Hamiltonian structure. To such a system there...
AbstractWe establish a close relationship between hamiltonian systems of hydrodynamic type and hyper...
The aim of this article is to classify pairs of the first-order Hamiltonian operators of Dubrovin-No...
We point out a pair of coupled KdV equations which admits a bi-Hamiltonian structure. © 1990 Società...
We define a new class of solutions to the WDVV associativity equations. This class is selected by th...
The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. ...
Abstract. We prove a simple condition under which the metric corresponding to a diagonalizable semi-...
none2siThe Oriented Associativity equation plays a fundamental role in the theory of Integrable Sys...
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 sup...
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian st...
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