Functions and Analysis


A Possible Theory of Partial Differential Equations

Authors: Robert Jackson

The current gold standard for solving nonlinear partial differential equations, or PDEs, is the simplest equation method, or SEM. As a matter of fact, 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 a new precedence with respect to 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, Ring and Knot theory in the finding of solutions to PDEs. Then the novel technique is applied in the derivation of new solutions to the Benjamin-Ono, QFT and Good Boussinesq equations. Finally, the study concludes via a discourse on the reasons why the technique is likely better than SEM and G'/G-expansion method, the scope and range of what GFT could ultimately accomplish, and the elucidation of a putative new branch of calculus, called "diversification".

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Submission history

[v1] 2019-10-05 16:37:37
[v2] 2019-10-10 16:25:43
[v3] 2019-10-15 10:26:40
[v4] 2019-10-19 11:43:00
[v5] 2019-11-06 19:11:42

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