Multiple invariant solutions of the 3D potential Yu–Toda–Sasa–Fukuyama equation via symmetry technique

Abstract

This paper studies the potential form of the 3D potential Yu–Toda–Sasa–Fukuyama equation through the perspective of Lie symmetry analysis. This technique combined with symbolic computations does prove that the general Lie operator depends on five parameters and six independent arbitrary functions that are variable in respect to time. The group invariant solutions associated to some 1D subalgebras are systematically construct and they do involve arbitrary functions. When these functions are expressed under several specific forms, the associated wave solutions possess multiple structures. Graphical representations of some particular solutions are as well provided. As far as we know such general solutions are presented here for the first time and do indicate the symmetry method to be applied in order to solve other multidimensional, integrable, or nonintegrable nonlinear dynamical models.