Nonisentropic Solutions of Simple Wave Type of the Gas Dynamics Equations

Periodic solutions from Lie symmetries for the generalized Chen-Lee-Liu equation

“…Furthermore, Lie symmetries can be applied to construct conservation laws [9][10][11]; to determine new solutions from old solutions [12] and many other [4]. There are various important results in the literature on the application of Lie's theory in mathematical physics and applied mathematics [13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Symmetry analysis for the $2+1$ generalized quantum Zakharov-Kuznetsov equation

“…The existence of transformations which leave invariant a differential equation indicates the existence of invariant functions which can be used to write the corresponding differential into an simpler form or into the form of another, well-known, differential equation. The theory of symmetries provide a systematic way which has been applied the last decades in a plethora of differential equations in all areas of applied mathematics, we refer the reader to [5][6][7][8][9][10][11][12][13][14][15][16] and references therein. For other methods on the derivation of analytic solutions for differential equations we refer the reader in [17][18][19][20][21] and references therein.…”

Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations

“…Consequently, Lie's theory is essential for various physical theories, from classical mechanics, quantum mechanics, fluid theory and many other [5,6,7,8,9,10,11,12,13,14]. Additionally, because the analysis of the Lie symmetries is a systematic way for the determination of exact and analytic solutions of nonlinear differential equations, it plays an important role in all theories of applied mathematics, we refer the reader in [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] and references therein.…”