A possible theory of partial differential equations 

Robert Lloyd Jackson II, Medical Doctorate (9427 W. 161st Terrace, Stilwell, Kansas 66085), E-mail: rljacksonmd@gmail.com 

517.95 

10.21685/2072-3040-2021-3-3 

The current gold standard for solving [nonlinear] partial differential equations, or [N]PDEs, is the simplest equation method, or SEM. Another prior technique for solving such equations, the G'/G-expansion method, appears to branch from the simplest equation method (SEM). This study discusses a new method for solving PDEs called the generating function technique (GFT) which may establish new precedence concerning SEM. First, the study shows how GFT relates to SEM and the G'/G-expansion method. Next, the paper describes a new theorem that incorporates GFT and Ring theory in the finding of solutions to PDEs. Then the novel technique is applied in the derivation of new or exotic solutions to the Benjamin-Ono, a QFT (nonlinear Klein-Gordon), and Good Boussinesq-like equations. Finally, the study concludes via a discourse on the reasons why the technique is better than SEM and G'/G-expansion method and the scope and range of what GFT could accomplish in the realm of mathematics, specifically differential equations. 

differential equations, generating function technique, G'/G-expansion method, simplest equation method 

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