New Group Structure of Compatible Systems of First Order Partial Differential Equations

Mr. Sagar Waghmare; Dr. Ashok Mhaske; Mr. Amit Nalvade; Smt. Todmal Shilpa

doi:https://doi.org/10.14445/22315373/IJMTT-V67I9P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 9 | Year 2021 | Article Id. IJMTT-V67I9P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I9P513

New Group Structure of Compatible Systems of First Order Partial Differential Equations

Mr. Sagar Waghmare, Dr. Ashok Mhaske, Mr. Amit Nalvade, Smt. Todmal Shilpa

Citation :

Mr. Sagar Waghmare, Dr. Ashok Mhaske, Mr. Amit Nalvade, Smt. Todmal Shilpa, "New Group Structure of Compatible Systems of First Order Partial Differential Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 9, pp. 114-117, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I9P513

Abstract

Group theory plays a vital role in mathematics, physics, chemistry, and computer science. Group theory has applications in geometry, symmetry and transformation puzzles like Rubik's Cube. Partial differential equations are used in problems involving functions of several variables, such as heat or sound, elasticity, electrodynamics, fluid flow, etc. In this article we have established relation between first order partial differential equations and group theory. If g(x,y,z,p,q) is the given first order partial differential equation, the set of all partial differential equations f(x,y,z,p,q) which are compatible with g(x,y,z,p,q) form group under usual addition of two functions. Furthermore this group forms an Abelian group.

Keywords

Group, Structure, Abelian, Compatible, Partial Differential

References

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