24 citations · 59 across the 6 of their papers we have counts for
8 papers · 1 filter
On steady motions of an ideal fibre-reinforced fluid in a curved stratum. Geometry and integrability
Dmitry K. Demskoi, Wolfgang K. Schief
It is shown that the kinematic equations governing steady motions of an ideal fibre-reinforced fluid in a curved stratum may be expressed entirely in terms of the intrinsic Gauss e…
The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System
Dmitry K. Demskoi
We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination of shifts from the two symmetries of the lattice sine-Gordon equ…
Darboux integrability of determinant and equations for principal minors
Dmitry K. Demskoi, Dinh T. Tran
We consider equations that represent a constancy condition for a 2D Wronskian, mixed Wronskian-Casoratian and 2D Casoratian. These determinantal equations are shown to have the num…
Quad-equations and auto-Bäcklund transformations of NLS-type systems
Dmitry K Demskoi
Treating an integrable quad-equation along with its two generalised symmetries as a compatible system allows one to construct an auto-Bäcklund transformation for solutions of the r…
On non-Abelian Toda model and related hierarchies
Dmitry K. Demskoi, Jyh-Hao Lee
We study limiting cases of the two known integrable chiral-type models with tree-dimensional configuration space. One of the initial models is the non-Abelian Toda mode…
On application of Liouville type equations to constructing Bäcklund transformations
Dmitry K. Demskoi
It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the Bäcklund transformations. Several new examples of such transforma…
On recursion operators for elliptic models
Dmitry K. Demskoi, Vladimir V. Sokolov
New quasilocal recursion and Hamiltonian operators for the Krichever-Novikov and the Landau-Lifshitz equations are found. It is shown that the associative algebra of quasilocal rec…
The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries, and more
Artur Sergyeyev, Dmitry Demskoi
We found a new symplectic structure and a recursion operator for the Sasa--Satsuma equation widely used in nonlinear optics, $$ p_t=p_{xxx}+6 p q p_x+3 p (p q)_x,\quad q_t=q_{xxx}+…