
The problem of complex meaning nonlinear equation in quotiend derivatives
Several ways of finding of the exact solutions inherent in the equations with soliton like solutions were applied to the given equation. In particular the presence of property of Penleve in the equation was conducted, solutions in the form of numbers of Lorana, exact solutions in the form ...

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 ...

A Lax pair for the (1+3) nonlinear equation
... and physics. The discovery of inverse scattering method played an important role in reconsidering the place of integrable systems of nonlinear partial differential equations in mathematical sciences. The search for a systematic approach to developing exact solutions of such systems has become one of the main problems in the theory of integrable systems.
1. Fokas A. S. Symmetries and integrability // Stud. Appl. Math. 77. 1987. No. 3. P. 253—299.
2. Солитоны и метод обратной задачи ...

One method for constructing exact solutions of equations of twodimensional hydrodynamics of an incompressible fluid
We propose a simple algebraic method for constructing exact solutions of equations of twodimensional hydrodynamics of an incompressible fluids.The problem reduces to consecutively solution three linear partial differential equations for a nonviscous fluid and to solving three linear partial differential equations ...

A surprising tale of longperiodic spin oscillations in the synthetic antiferromagnets: some exact solutions
... collisions between the magnetic domains of different spin orientations ( and ). The resulting model comprised of a system of nonlinear differential equations is closely examined, after which we propose a simple analytical method of construction of its exact solutions. This method is shown to generate an infinite family of solutions associated with the degenerate hypergeometric functions, parameterized by a natural number N. One of those solutions with N = 2 produces the magnetization function which perfectly ...

New classes of exact solutions and consistent models of cosmological evolution
... of these equations as a secondorder linear differential equation. Particularly, the method allows to construct a more general solution, parametrized by two constants, using any known solution. Also it is shown, that in a specific case new classes of exact solutions have singularities with the following property: a geodesic, which begins or ends in the singularity, has an infinite length. Such a singularity leads to an absence of event horizons (if this is a future singularity). In this case it might prove ...

The dynamics of chiral cosmological fields in the canonical phantom model
... Cosmol. 2005. Vol. 11. P. 329—332.
17. Chervon S. V., Fomin I. V. On calculation of the cosmological parameters in exact models of inflation // Grav. Cosmol. 2008. Vol. 14. P. 163.
Fomin I. V., Chervon S. V., Krukov S. V.
inflation, scalar field, exact solutions, gravitational waves
7480

An impacton solution for the vortex filament
A new way of construction of exact solutions describing the shape and the dynamics of vortex filaments is described. The new method is based on application of a binary Darboux transformation to the solutions of the nonlinear Schrödinger equation. A new type of solutions is constructed: ...

A solution of the transport task in relation to the cargo rail transportation
... Scheduling the Rounds of a Rolling Mill. Pittsburgh, PA, 1986.
2. Fischetti M., Toth P. An additive approach for the optimal solution of the prizecollecting travelling salesman problem // Vehicle Routing: Methods and Studies. NorthHolland, 1988. P. 319–343.... ... traveling salesman problem: II. Polyhedral results // Ibid. 1995. Vol. 25. P. 199–216.
5. Focacci F., Lodi A., Milano M. A hybrid exact algorithm for the TSPTW // INFORMS Journal on Computing. 2002. № 14 (4). Р. 403—417.
6. BarYehuda R., Evenb G., Shahar ...

An integrable case of the Schrödinger matrix equation for multilevel quantum systems
... 16—22.
4.
Зайцев А.
А.
Лекции по теории динамических систем: учеб. пособие. Калининград, 2004.
Zaitsev A. A., Kargapolov D. A.
Schrödinger equation, multilevel quantum system, exact solution, invariant, characteristic equation.
1826

An application of the Abel equation of first type to the task of solving the Friedman equations
... Lösungsmethoden und Lösungen // Chelsea Publishing Co, New York. 1959.
7
.
Sachdev P.
L.
A Compendium of Nonlinear Ordinary Differential Equations // John Wiley & Sons, 1997.
8.
Chervon S.
V., Zhuravlev V.
M., Shchigolev V.
K.
New exact solutions in standard inflationary models // Phys. Lett. B398. (1997) 269—273.
9.
Felder G., Frolov A.
et al. Cosmology With Negative Potentials // Phys. Rev
.
D
66 (2002) 023507.
Yurov V. A.
Abel equation, EinsteinFriedmann equations, scalar ...

The dynamics of localized pulse as solutions of Davey — Stewartson II equations
.... 216—228.
8.
(Charles) Li Ya., Yurov A.
V.
Lax pairs and Darboux transformations for Euler equations // Studies in Applied Mathematics. 2003. Т. 111, №
1. P. 101—113.
9.
Yurov A.
V., Yurova A.
A.
One method for constructing exact solutions of equations of twodimensional hydrodynamics of an incompressible fluid // Theoretical and Mathematical Physics. 2006. Т. 147, №
1. P. 501—508.
10.
Bordag M., Yurov A.
Spontaneous symmetry breaking and reflectionless scattering ...

Exultonlike solution and two phase of collapse of an intrusive lens
....
К вопросу о динамике вихревой нити // Интрузионные течения: теория и эксперимент. Калининград
, 1997.
С
. 102—111.
2.
Yurova A.
A., Gritsenko V.
A.
Novel Exact Solutions Describing the Evolution of Lenses Frontal Vorticity. Oceanic Fronts and Related Phenomena. Konstantin Fedorov Memorial Sympozium. 18—22 May 1998, Pushkin, St.Petersburg. Abstracts of the reports.
St. Petersburg
, RSHMU Publishers, 1998....

The Abel equation and cosmological scalar field zeroes
... Yurov V. A., Chervon S. V., Sami M. Total energy potential as a superpotential in integrable cosmological models // Theoretical and Mathematical Physics. 2011. Vol. 166, Iss. 2. P. 299—311.
9. Chervon S. V., Zhuravlev V. M., Shcigolev V. K. New Exact Solutions in Standart Inflationary Models // Phys. Lett. B. 1997. Vol. 395. P. 269—273.
Yurov V., Yaparova A.
cosmology, Abel equation, scalar field.
3036

The bottom gravitational stream on inclined bottom in Ecmann approximation
The article examines the deduction and the scope of the equation describing the dynamics of a thin layer of liquid over inclined bottom
in the framework of Eckman’s approach and obtains exact solutions in the form of travelling waves. The author makes a conclusion this equation
is nonintegrable on the basis of Painlevé analysis.
1.
Nof D., Paldor N., Van Golder S. Abyssal Gyres
// Geophys. Astrophys. Fluid Dynamics. 1991. V. 58. P. ...

On the relations between the integrable hierarchies
... 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
4853

Oscillations, resonances and waves in a nonlocal medium with sources
New exact solutions are obtained for a spatially nonlocal wave equation with sources. The results are set out in the terms of the heat transfer theory. The nonlocality of the problem is determined by the value of the fourth spatial derivative. We considered two ...

Decay of a weak gap and wave propagation in a nonlocal environment with a source
... sonic, supersonic) is determined with respect to the velocity of propagating heat perturbations. We give examples of the exact solving the problem of disintegration of a weak discontinuity in the temperature field. This problem is set as follows. ... ... Conf. of Robot, Vision and Signal Processing. 2015. P. 71—74.
14. Mochnacki B., Ciesielski M., PiaseckaBelhayat A. Numerical solution of the bioheat transfer equation with uncertain parameters using the sensitivity analysis method // Defect and Diffusion ...

Portfolio optimization in the case of an exponential utility function and in the presence of an illiquid asset
... group analysis of differential equations. CRS Press, 1994.
12. Jacod J., Shiryaev A. N. Limit theorems for stochastic processes. (Grundlehren der mathematischen Wissenschaften ; Vol. 288). Springer, 2002.
13. Meleshko S. V. Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering. Springer, 2005.
14. Meleshko S. V., Moyo S. On the complete group classification of the reactiondiffusion equation with a delay ...