arXiv subjects

L. V. Bogdanov

Publications and source records attributed to L. V. Bogdanov.

40 records · Page 3Linked to original sources

arXiv1996

Generalized integrable hierarchies and Combescure symmetry transformations

Unifying hierarchies of integrable equations are discussed. They are constructed via generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical meaning, are in fact the symmetry transformations of generalized integrable hierarchies. Generalized equation written in terms of invariants of Combescure transformations are the usual integrable equations and their modified partners. The KP-mKP, DS-mDS hierarchies and Darboux system are considered.

solv-int↗

arXiv1995

Generalized Hirota bilinear identity and integrable q-difference and lattice hierarchies.

Hirota bilinear identity for Cauchy-Baker-Akhieser (CBA) kernel is introduced as a basic tool to construct integrable hierarchies containing lattice and q-difference times. Determinant formula for the action of meromorphic function on CBA kernel is derived. This formula gives opportunity to construct generic solutions for integrable lattice equations.

q-alg↗

arXiv1995

Lattice and q-difference Darboux-Zakharov-Manakov systems via $\bar{\partial}$-dressing method

A general scheme is proposed for introduction of lattice and q-difference variables to integrable hierarchies in frame of $\bar{\partial}$-dressing method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov systems of equations are derived. Darboux, Bäcklund and Combescure transformations and exact solutions for these systems are studied.

solv-int↗

arXiv1994

Generic solutions for some integrable lattice equations

We derive the expressions for $ψ$-functions and generic solutions of lattice principal chiral equations, lattice KP hierarchy and hierarchy including lattice N-wave type equations. $τ$-function of $n$ free fermions plays fundamental role in this context. Miwa's coordinates in our case appear as the lattice parameters.

hep-th↗