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Sergei B. Leble

Publications and source records attributed to Sergei B. Leble.

3 recordsLinked to original sources
arXiv2001

Dressing chain equations associated to difference soliton systems

The dressing chain equations for factorizing operators of a spectral problem are derived. The chain equations itselves yield nonlinear systems which closure generates solutions of the equations as well as of the nonlinear system if both operators of the correspondent Hirota bilinearization are covariant with respect to Darboux transformation which hence defines a symmetry of the nonlinear system as well as of these closed chains. Examples of Hirota and Nahm equations are specified.

math-ph↗
arXiv1999

Division of Differential operators, intertwine relations and Darboux Transformations

The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The expresions of classic Bell polinomils via generalized one is given. The conditions of an exact factorization possibility leads to the intertwine relation and results in some linearizable generalized Burgers equation. An alternative proof of the Matveev theorem is given and Darboux - Matveev transformations formula for coefficients follows from the intertwine relations and also expressed in the generalized Bell polinomials.

math-ph↗