Nonlocal transformations with additional variables. Forced symmetries - Tychynin, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.9: 519.46The concept of nonlocal transformation with additional variables is offered, developed and applied to search additional symmetry of nonlinear partial differential equations. Possible schemes of relation of differential equations by means of prolonged nonlocal transformations of this type are considered, several examples are given. The method is used for constructing algorithms and formulas generating new solutions from known solutions that use additional symmetry. These formulas are applied to finding of exact solutions for some nonlinear equations.