Results: **5**

#### New classes of exact solutions and consistent models of cosmological evolution

... точно решаемые космологические модели // Теоретическая и математическая физика. 2004. Т. 139, № 3. С. 405—422.
4. Yurov A. V., Yurov V. A. Nonsingular Brane Solutions via the **Darboux** **Transformation** // Phys. Rev. D. 2005. Vol. 72, iss. 2. 026003.
5. Andrianov A. A., Cannata F., Kamenshchik A. Y. Smooth Dynamical Crossing of the Phantom Divide Line of a Scalar Field in Simple Cosmological Models // Phys. Rev. D. 2005. Vol. 72, iss. ...

#### Closed lattice of Toda equations

... lattices in one and two spatial dimensions. Using the modified Toda equations m0TCand m1TC as an example, it is shown that the combination of the **Darboux** and Schlesinger **transformations** leads to closed dressing chains.
1. Matveev V. B., Salle M. A. **Darboux** **Transformations** and Solitons. Berlin ; Heidelberg, 1991.
2. Yurov A. V., Yurov V. A. The Landau-Lifshitz Equation, the NLS, and the Magnetic Rogue Wave as a By-Product of Two Colliding Regular «Positons» // Symmetry. 2018. Vol. 10, iss. 4, 82. arXiv: ...

#### System analysis and methodology for developing a software product of a mathematical model of physical processes for the aviation industry

... lattices in one and two spatial dimensions. Using the modified Toda equations m0TCand m1TC as an example, it is shown that the combination of the **Darboux** and Schlesinger **transformations** leads to closed dressing chains.
1. Matveev V. B., Salle M. A. **Darboux** **Transformations** and Solitons. Berlin ; Heidelberg, 1991.
2. Yurov A. V., Yurov V. A. The Landau-Lifshitz Equation, the NLS, and the Magnetic Rogue Wave as a By-Product of Two Colliding Regular «Positons» // Symmetry. 2018. Vol. 10, iss. 4, 82. arXiv: ...

#### Generation of exact solutions of Fridman equations leading to Cardy–Verlinde formula by **Darboux** **transformation**

It is considered a possibility of generation of exact solutions for Friedman equations by **Darboux** **transformation**, for which Cardy — Verlinde formula is valid. Two modifications of **Darboux** **transformation** are offered, which let generate such solutions. Exact solutions are obtained, for which Cardy — Verlinde formula is valid at least near some singularities....

#### Initial problem for heat equation with multisoliton inhomogeneity and one-loop quantum corrections

... covariance of the heat equation and used to evaluate the correspondent functional integral in quasiclassical approximation. Quantum corrections to a kink-like solutions of Landau — Ginzburg model are calculated.
Leble S. B., Yurov A. V.
**Darboux** **transformation**, heat conduction equation, kink, functional integral
76-79