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In this paper, we investigate the algebraic and geometric properties of the hyperbolic Toda equations u xy = exp(Ku) associated with nondegenerate symmetrizable matrices K. A hierarchy of analogs to the potential modified Korteweg–de Vries equation u t = u xxx + u 3 x is constructed, and its relation with the hierarchy for the Korteweg–de Vries equation T t… (More)

- A V Kiselev
- 2004

Properties of Hamiltonian symmetry flows on hyper-bolic Euler-type equations are analyzed. Their Lagrangian densities are demonstrated to supply the Hamiltonian operators for subalgebras of their Noether symmetries, while substitutions between Euler-type equations define Miura transformations between the symmetry flows; some Miura maps for Liouvillean… (More)

We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws,… (More)

Representations of the Schlessinger–Stasheff's associative homotopy Lie algebras in the spaces of higher–order differential operators are analyzed. The W-transformations of chiral embeddings, related with the Toda equations, of complex curves into the Kähler manifolds are shown to be endowed with the homotopy Lie algebra structures. Extensions of the… (More)

- A V Kiselev, T Wolf
- 2008

We consider nonlinear, scaling-invariant N = 1 boson+fermion supersymmetric systems whose right-hand sides are homogeneous differential polynomials and satisfy some natural assumptions. We select the super-systems that admit infinitely many higher symmetries generated by recursion operators; we further restrict ourselves to the case when the dilaton… (More)

A classification problem is proposed for supersymmetric evolutionary PDE that satisfy the assumptions of nonlinearity, nondegeneracy, and homogeneity. Four classes of nonlinear coupled boson-fermion systems are discovered under the weighting assumption |f | = |b| = |D t | = 1 2. The syntax of the Reduce package SsTools, which was used for intermediate… (More)

An algebraic definition of Gardner's deformations for completely inte-grable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found.… (More)

A classification problem is proposed for supersymmetric scaling-invariant evolutionary PDE that satisfy the assumptions of nonlinearity and nondegeneracy. Four classes of nonlinear coupled boson-fermion systems are discovered under the homogeneity assumption |f | = |b| = |D t | = 1 2. The syntax of the Reduce package SsTools, which was used for intermediate… (More)

- Arthemy V Kiselev, Johan W Van De Leur
- 2009

For the 3-component dispersionless Boussinesq-type system, we construct two compatible nontrivial finite deformations for the Lie algebra structure in the symmetry algebra. Introduction. In this short note we construct a two-parametric family of nontrivial finite deformations for the Lie bracket in the algebra of symmetries for the 3-component… (More)