@inproceedings{6546cca6d5104503b99669685a523b3f,
title = "Partially nonclassical method and conformal invariance",
abstract = "A generalization of the classical and nonclassical methods for finding similarity reductions of a partial differential equation (PDE), termed as the {"}partially nonclassical method{"}, is developed. Applying the partially nonclassical method to the flat steady-state boundary layer (BL) equations shows that the partially nonclassical method enables one to obtain similarity reductions obtainable neither classical nor nonclassical methods. Based on the observation, that applying the classical Lie group method to a PDE yields transformations which do not leave the PDE invariant but modify it by a conformal factor, a unified representation of the classical, nonclassical and partially nonclassical methods for finding similarity reductions of PDEs is given. That representation may lead to further generalizations of the nonclassical method.",
keywords = "Generalized Kaup-Kupershmidt Solitons, Integrability, KdV type equations, Multisoliton solutions, Static solitons",
author = "Burde, {Georgy I.}",
note = "Publisher Copyright: {\textcopyright} 2019 Author(s).; International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 ; Conference date: 13-09-2018 Through 18-09-2018",
year = "2019",
month = jul,
day = "24",
doi = "10.1063/1.5114174",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "T.E. Simos and T.E. Simos and T.E. Simos and T.E. Simos and Ch. Tsitouras and T.E. Simos",
booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018",
}