Optimal system, invariant solutions and evolution of weak discontinuity for isentropic drift flux model

Study of wave propagation in arterial blood flow under symmetry analysis

“…This approach for deriving the optimal system is also pursued by Sekhar and Satapathy. 17 For the exact solution of PDEs arising in many physical phenomena, using symmetry analysis and Riemann problem, we refer Bira et al 18,21 and Sahoo et al, 19,20 whereas the evolutionary behavior of weak discontinuities and elementary wave interaction for quasi-linear hyperbolic systems, we refer Raja et al, 22 Satapathy and Sekhar, 23 Zeidan and Bira, 24 and Sil and Raja Sekhar. 25 The structure of this article is as follows: Section 2 deals with a brief discussion on the model along with the derivation of the symmetry group of transformations.…”

Optimal Subalgebra of GKP by Using Killing Form, Conservation Law and Some More Solutions

“…Exact solutions of such systems can help in a better way to explain their complicated physical phenomena and the dynamical processes modeled by them. For instance, among the past researches [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], exact solutions of NPDEs play a vital role in the study of these complex physical phenomena. This literature review includes the previous findings [1][2][3][4][5][6][7][8][9][10][11][12] during the last decade.…”

Similarity reductions, new traveling wave solutions, conservation laws of (2+1)- dimensional Boiti-Leon-Pempinelli system

“…Once one has determined the symmetry group of a system of differential equations, based on it variety of applications are available. One of the most important and useful application of symmetry method is to obtain systematically some classes of exact solutions [2,3,4,5,6]. A particular solution obtained from symmetry group G is group invariant solution corresponding to the group G. For a given PDE system there may exist infinitely many particular solutions, so one needs to minimize the search for exact solutions.…”