A Bäcklund transformation for the Burgers hierarchy.
A critical phenomenon in solitonic Ising chains.
A differential geometric setting for dynamic equivalence and dynamic linearization
This paper presents an (infinite-dimensional) geometric framework for control systems, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise: equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framework that dynamic equivalence of single-input systems is the same as static equivalence.
A discrete variational approach for investigation of stationary localized states in a discrete nonlinear Schrödinger equation, named IN-DNLS.
A dynamical system connected with inhomogeneous 6-vertex model
A generalised Hopf algebra for solitons.
A generalization for Peakon's solitary wave and Camassa-Holm equation.
A gentle (without chopping) approach to the full Kostant-Toda lattice.
A global factorization theorem for the ZS-AKNS system.
A Hopf bifurcation of interfaces in a Dirichlet problem.
A KAM theorem for infinite-dimensional discrete systems.
A look on some results about Camassa–Holm type equations
We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.
A new hierarchy of integrable system of dimensions: from Newton's law to generalized Hamiltonian system. II.
A note on the rotationally symmetric SO(4) Euler rigid body.
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation.
A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
A special case of the Garnier system, -polarized abelian surfaces and their moduli
A survey of Nambu-Poisson geometry.
A survey on Nambu-Poisson brackets.
A vertex operator approach for form factors of Belavin's -symmetric model and its application.