
Numerical solution of the Schrödinger equations with polynomial potentials (Part II)
The algorithm of the numerical realization of a fundamental solution of a Cauchy problem for the onedimensional Schrodinger equation with polynomial potentials is described. The stationary Schrodinger equation for a proton in the double potential well is solved by using Ritz variation method. The Green’s function is formed on a ...

Numerical solution of the Schrödinger equations with polynomial potentials (Part I)
The fundamental solution of a Cauchy problem and the spectral task for a onedimensional Schrodinger equations with potential in the form of polynomials m P (x) (m 6) is solved. Numerical calculations are applied to modelling adiabatic potentials with two minima characteristic for a ...

Numerical simulation of forming and evolution of solitons in chain of nucleotide couples
The Cauchy’s problem of the induced charge movement along the discrete chain of nucleotide couples in DNA is solved in the frame of Holstein’s model taking account surrounding temperature fluctuations. For the initial conditions chosen specifically the evolution ...

On the relations between the integrable hierarchies
... 262. P. 445–452.
13. Leble S. B., Yurov A. V. Reduction Restrictions of Darboux and Laplace Transformations for the Goursat Equation // Journal of Mathematical Physics. 2002. Vol. 43, № 2. P. 1095–1105.
14. Yurov V. A., Yurov A. V. The Cauchy problem for the generalized hyperbolic NovikovVeselov equation. arXiv:1509.06078 [nlin.SI].
Yurov A., Yurova A.
Lax pair, nonlinear partial differential equation, exact solution, integrable equation
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Closed lattice of Toda equations
... E. On One Analogue of the Moutard Transformation for the Goursat Equation // Theor. Math. Phys. 1999. Vol. 122, iss. 1. P. 39—45.
18. Athorne C., Nimmo J. J. C. On the Moutard Transformation for Integrable Partial Differential Equations // Inverse Problems. 1991. Vol. 7, iss. 5. P. 809—826.
19. Юров А. В. Преобразование Бэклунда — Шлезингера для уравнений Дэви — Стюартсона // Теоретическая и математическая ...

System analysis and methodology for developing a software product of a mathematical model of physical processes for the aviation industry
... E. On One Analogue of the Moutard Transformation for the Goursat Equation // Theor. Math. Phys. 1999. Vol. 122, iss. 1. P. 39—45.
18. Athorne C., Nimmo J. J. C. On the Moutard Transformation for Integrable Partial Differential Equations // Inverse Problems. 1991. Vol. 7, iss. 5. P. 809—826.
19. Юров А. В. Преобразование Бэклунда — Шлезингера для уравнений Дэви — Стюартсона // Теоретическая и математическая ...