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V. A. Zolotarev

Publications and source records attributed to V. A. Zolotarev.

5 recordsLinked to original sources
arXiv2025

Inverse scattering problem for a third-order differential operator with double potential

Direct and inverse scattering problems for a third-order self-adjoint differential operator on the whole axis are studied. This operator is the sum of three summands: operator of third derivative, operator of multiplication by a function, and operator of multiplication by derivative of a function. For the solution of the inverse scattering problem, two closed systems of linear integral equations are obtained. Knowing solutions to these systems, using explicit formulas, methods of restoration of both potentials on half-axes $\mathbb{R}_\pm$ are specified.

math.CA↗
arXiv2024

Inverse scattering problem for third order differential operators on the whole axis

Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This system contains scattering coefficients and bound state elements as independent parameters. Form of the simplest reflectionless potential (analogous to soliton) is found.

math.CA↗
arXiv2023

$p$-Hyperbolic Zolotarev Functions in Boundary Value Problems for a $p\,$th order Differential Operator

For the self-adjoint operator of the $p$th derivative, a system of fundamental solutions is constructed. This system is analogues to the classical system of sines and cosines. The properties of such functions are studied. Classes of self-adjoint boundary conditions are described. For the operator of the third derivative, the resolvent is calculated and an orthonormal basis of eigenfunctions is given.

math.FA↗