Ismagil Habibullin
Publications:
Habibullin I. T., Khakimova A. R.
Higher Symmetries of Lattices in 3D
2024, vol. 29, no. 6, pp. 853-865
Abstract
It is known that there is a duality between the Davey – Stewartson type coupled
systems and a class of integrable two-dimensional Toda type lattices. More precisely, the coupled
systems are generalized symmetries for the lattices and the lattices can be interpreted as dressing
chains for the systems. In our recent study we have found a novel lattice which is apparently
not related to the known ones by Miura type transformation. In this article we describe higher
symmetries to this lattice and derive a new coupled system of DS type.
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Habibullin I. T., Khakimova A. R.
Abstract
An original effective method for constructing explicit solutions of integrable Davey –
Stewartson type equations is proposed, based on the use of dressing chains. The main difficulty
arising when using the symmetry approach in 3D is associated with nonlocal variables entering
the equation. To solve the nonlocality problem, it is proposed to replace the infinite dressing
chain with its finite-field reductions preserving the integrability property. The application of
the method is illustrated by the DS I equation, for which a new class of explicit solutions
is constructed that depend on two arbitrary functions. In this example, the dressing chain is
replaced by a finite-field reduction of the Toda lattice corresponding to a simple Lie algebra $A_2$.
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