Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

Lie Algebra Techniques Using both Variational and Non-Variational Methods

Abstract

Patrick Serwene

Numerous variations of physical issues, such as those in fluid dynamics, solid mechanics, plasma physics, quantum field theory, as well as in mathematics and engineering, include nonlinear partial differential equations. Systems of nonlinear partial differential equations have also been shown to appear in chemical and biological applications. The analytical analysis of a fully generalised (3+1)-dimensional nonlinear potential Yu- Toda-Sasa-Fukuyama equation, with applications in physics and engineering, is presented in this article. In contrast to earlier study on the problem that has already been done, the extended form of the potential Yu-Toda-Sasa-Fukuyama equation is investigated in greater detail in this paper, leading to the achievement of many novel solutions that are of interest. The nonlinear partial differential equation is fundamentally reduced to an integrable form by the use of the Lie group theory, allowing for direct integration of the outcome.