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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-9
Year of Publication : 2021
Authors : Mr. Sagar Waghmare, Dr. Ashok Mhaske, Mr. Amit Nalvade, Smt. Todmal Shilpa
  10.14445/22315373/IJMTT-V67I9P513

MLA

MLA Style: 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 67.9 (2021):114-117. 

APA Style: Mr. Sagar Waghmare, Dr. Ashok Mhaske, Mr. Amit Nalvade, Smt. Todmal Shilpa(2021). New Group Structure of Compatible Systems of First Order Partial Differential Equations  International Journal of Mathematics Trends and Technology, 67(9), 114-117.

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. 

Reference

[1] Craddock, Mark. Symmetry Groups of Linear Partial Differential Equations and Representation Theory: The Laplace and Axially Symmetric Wave Equations. Journal of Differential Equations, (2000).
[2] LAHNO, P. BASARAB–HORWATH and V. Group Classification of Nonlinear Partial Differential Equations: a New Approach to Resolving the Problem. Proceedings of Institute of Mathematics of NAS of Ukraine 43 (2002) 86–92.
[3] Chandradeepa Chitalkar, Vasant R. Nikam. Research paper : Solution of fractional partial differential equations using iterative method., Fractional Calculus and Applied Analysis, (2012).

Keywords : Group, Structure, Abelian, Compatible, Partial Differential