Roadmap of the Multiplier Method for Partial Differential Equations

Juan Arturo Alvarez-Valdez () and Guillermo Fernandez-Anaya ()
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Juan Arturo Alvarez-Valdez: Department of Physics and Mathematics, Universidad Iberoamericana Ciudad de México, Lomas de Santa Fe, Ciudad de México 01219, Mexico
Guillermo Fernandez-Anaya: Department of Physics and Mathematics, Universidad Iberoamericana Ciudad de México, Lomas de Santa Fe, Ciudad de México 01219, Mexico

Mathematics, 2023, vol. 11, issue 22, 1-57

Abstract: This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking.

Keywords: multipliers; mathematics; applied mathematics; partial differential equations; Noether’s Theorem; conservation laws; symmetries; literature compilation; symmetry actions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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