Sokil B. I.
On the application of Ateb-functions to the construction of an asymptotic solution of the perturbed nonlinear Klein-Gordon equation
Mitropolskiy Yu. A., Sokil B. I.
Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 665–670
For the perturbed nonlinear Klein-Gordon equation, we construct an asymptotic solution by using Ateb-functions. We consider autonomous and nonautonomous cases.
On asymptotic approximation of a solution of a boundary-value problem for a nonlinear nonautonomous equation
Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1580–1583
On the basis of periodic Ateb functions, in the resonance and nonresonance cases, we construct the asymptotic approximation of one-frequency solutions of a boundary-value problem for a nonlinear nonautonomous equation.
On the application of Ateb-functions to the construction of a solution of a nonlinear Klein-Gordon equation
Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 872–877
For a nonlinear Klein-Gordon equation, we construct the first approximation of an asymptotic solution by using Ateb-functions. The resonance and nonresonance cases are considered.
Application of ateb-functions to the construction of solutions of some nonlinear partial differential equations
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 287-288
We construct asymptotic approximations of one-frequency solutions of some nonlinear partial differential equations by using periodic Ateb-functions.
On the construction of asymptotic approximations for a nonautonomous wave equation
Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1714–1716
For a nonautonomous wave equation with homogeneous boundary conditions, we construct one-frequency approximations of asymptotic solutions by using periodic Ateb-functions. Resonance and nonresonance cases are considered.
Construction of one-frequency solutions of boundary-value problems for a nonautonomous wave equation
Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1275–1279
By using special periodic Ateb-functions, we construct asymptotic representations of one-frequency solutions of boundary-value problems for a nonautonomous wave equation.
On a method for constructing one-frequency solutions of a nonlinear wave equation
Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 782–784
A method for constructing one-frequency solutions of nonlinear wave equations is suggested. This approach is based on a modified representation of asymptotic expansions by using special periodic Atebfunctions. This method makes it possible to obtain approximate solution of the problem under consideration without difficulty.
Asymptotic representation of the solution of a nonlinear system with resonance
Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 390 — 392
Asymptotic expansions of a boundary-value problem for a certain nonlinear partial differential equation
Ukr. Mat. Zh. - 1982. - 34, № 6. - pp. 803—805
An asymptotic expansion for a class of nonlinear differential equations
Ukr. Mat. Zh. - 1980. - 32, № 5. - pp. 686–693