2019
Том 71
№ 11

All Issues

Soltanov K. N.

Articles: 2
Article (English)

Integrability Analysis of a Two-Component Burgers-Type Hierarchy

Blackmore D., Özçağ E., Prykarpatsky A. K., Soltanov K. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 147-162

The Lax integrability of a two-component polynomial Burgers-type dynamical system is analyzed by using a differential-algebraic approach. Its linear adjoint matrix Lax representation is constructed. A related recursive operator and an infinite hierarchy of nonlinear Lax integrable dynamical systems of the Burgers–Korteweg–de-Vries type are obtained by the gradient-holonomic technique. The corresponding Lax representations are presented.

Article (English)

Global Existence and Long-Term Behavior of a Nonlinear Schrödinger-Type Equation

Soltanov K. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 1. - pp. 68–87

We study a global mixed problem for the nonlinear Schrödinger equation with a nonlinear term in which the coefficient is a generalized function. A global solvability theorem for the analyzed problem is proved by using the general solvability theorem from [K. N. Soltanov, Nonlin. Anal.: Theory, Meth., Appl., 72, No. 1 (2010)]. We also investigate the behavior of the solution of the problem under consideration.