Lie symmetry analysis of Burgers‐type systems

Kontogiorgis, Stavros; Sophocleous, Christodoulos

doi:10.1002/mma.4659

Cited by 4 publications

(1 citation statement)

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“…The theory of Lie symmetries was first initiated by Sophus Lie . Consequently, several generalizations of classical symmetry method including nonclassical method for various differential equations are developed. In this context, we indicate that Lie symmetry named as nonlocal symmetry is a very useful tool.…”

Section: Introductionmentioning

confidence: 99%

Optimal classification, exact solutions, and wave interactions of Euler system with large friction

Sahoo

Sekhar

2020

Math Methods in App Sciences

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We derive exact solutions of one-dimensional Euler system that accounts for gravity together with large friction. Certain optimal classes of subalgebra using Lie symmetry analysis are obtained for this system. We apply the reduction procedure to reduce the Euler system to a system of ordinary differential equations in terms of new similarity variable for each class of subalgebras leading to invariant solutions. The evolution of characteristic shock and its interaction with the weak discontinuity by using one of the invariant solutions is studied. Further, the properties of reflected and transmitted waves and jump in acceleration influenced by the incident wave have been characterized. KEYWORDS euler system with large friction, invariant solution, lie symmetry analysis, optimal classification, wave interactions, weak discontinuity MSC CLASSIFICATION 35A30; 35C05; 35L60; 35Q35; 76D33 Math Meth Appl Sci. 2020;43:5744-5757. wileyonlinelibrary.com/journal/mma

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Section: Introductionmentioning

confidence: 99%