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math-ph2023
Asymptotic step-like solutions to the singularly perturbed Burgers' equation
Valerii Samoilenko, Yuliia Samoilenko, Elvira Zappale
The paper deals with a problem of asymptotic step-like solutions to the Burgers' equation with variable coefficients and a small parameter. By means of the non-linear WKB method, t…
math-ph2018
Existence of solutions to non-homogeneous higher order differential equation in the Schwartz space
Valerii H. Samoilenko, Yuliia I. Samoilenko
There is studied problem on existence of solutions to non-homogeneous differential equation of higher even order. Similar problem arises while studying soliton and soliton-like sol…