Algorithm of constructing asymptotic solutions to Cauchy problem for singular perturbed Korteweg-de Vries equation with varying coefficients in case of even degree of small parameter is proposed.

[1] Gardner C.S., Green J.M., Kruskal M.D., Miura R.M. Method for solving the Korteweg-de Vries equation // Phys. Rev. Lett.- 1967.- 19 .- P. 1095-1098.

[2] Korteweg D.J., de Vries G. On the change in form of long waves advancing in a rectangular canal and a new type of long stationary waves // Philos. Mag.- 1895.- N39.- P.422-433.

[3] Scott-Russel J. Report on waves // Report of the fourteenth meeting of the British association for the advancement of science. - John Murray, London.- 1844.- P.311-390.

[4] Lax P.D. Integrals of nonlinear equations of evolution and solitary waves // Communications Pure Applied Mathematics.- 1968.- 21 , N15.- P.467-490.

[5] Zakharov V.E., Faddeev L.D. The Korteweg-de Vries equation is a completely integrable Hamiltonian system // Functional analysis and its applications. - 1971. - 5, N4. - P.18-27

[6] Novikov S.P. Periodic problem for the Korteweg-de Vries equation // Functional analysis and its applications. - 1974. - 8, N3. - P. 54-66.

[7] Zakharov V.E., Manakov S.V., Novikov S.P., Pitaevsky L.P. Soliton theory: A method of the inverse scattering problem. - M.: Nauka, 1980. - 320 p.

[8] Mitropolsky Yu.A., Bogolyubov N.N. (Jr.), Prikarpatsky A.K., Samoylenko V.G. Integrable dynamic systems: spectral and differential-geometric aspects. - Kiev: Naukova Dumka, 1987. - 296 p.

[9] Maslov V.P., Omelyanov G.A. Asymptotic soliton-like solutions of equations with small dispersion // Uspekhi matem. sciences. - 1981.- 36 (219), N2.- P.63-124.

[10] Samoilenko V.G., Samoilenko Y.I. Asymptotic expansions for single-phase soliton-like solutions of the Korteweg-de Vries equation with variable coefficients // Ukr. Mat. Zh. - 2005.- 58, N1.- P.111-124.

[11] Samoylenko V.Hr., Samoylenko Yu.I. Asymptotic solution to Cauchy problem for Korteweg- de Vries equation with varying coeficients and small dispersion // Computer algebra systems in teaching and research. Proceedings of 4-th International Workshop, CASTR 2007. - Siedlce: Wydavnictwo Akademii Podlaskiey. - 2007. - P.272-280.

[12] Samoilenko V.G., Samoilenko Yu.I. Asymptotic expansions for single-phase soliton-like solutions of the Cauchy problem for the Korteweg-de Vries equation with variable coefficients // Ukr. Mat. Zh.— 2007.— 59, N1.- P.122—132.

[13] Samoilenko Yu.I. Cauchy problem for the Korteweg-de Vries equation with variable coefficients and small dispersion // Scientific Bulletin of Chernivtsi University. Mathematics. Chernivtsi.- 2007.- 336 - 337.- P.170-177.

[14] Faminsky A.V. The Cauchy Problem for the Korteweg-de Vries Equation and its Generalizations // Proceedings of the I.G.Petrovsky Seminar. - 1988. - 13. - P.56-105.