Lie symmetry analysis, optimal system and invariant solutions of (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles

Invariance analysis, optimal system, and group invariant solutions of (3+1)‐dimensional non‐linear MA‐FAN equation

“…Satapathy and Raja Sekhar [34] solve Chaplygin gas equations with accurate answers. The authors in the literature [35, 36] used the Lie symmetry analysis to find some new exact solutions of the $$$ \left(3+1\right) $$$‐dimensional non‐linear water wave equation in liquid with gas bubbles and $$$ \left(2+1\right) $$$‐dimensional modified dispersive water wave (MDWW) equation. The authors found novel and precise solutions of compressible isentropic Navier–Stokes equation utilizing optimal subalgebras in Jiwari et al [37].…”

Symmetry analysis, optimal classification and dynamical structure of exact soliton solutions of (2+1)-dimensional modified Bogoyavlenskii–Schiff equation

“…These invariant solutions describe their behavior like they display its asymptotic nature and the information of the singularities if it exists. Thus, various efficient methods and techniques are there to obtain exact soliton solutions, such as inverse scattering transformation [1], Hirota bilinear method [2], nonlocal symmetry [3], Bäcklund transformation [3], Painlevé analysis [3], Lie symmetry method [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], etc.…”

Similarity transformations and linearization for a family of dispersionless integrable PDEs

“…There is a plethora of applications in the literature on the symmetry analysis of various dynamical systems. The method of symmetry analysis is applied in various systems of fluid dynamics in the studies [12][13][14][15][16][17][18][19][20][21][22][23][24]. The Burgers-heat system is investigated by applying the symmetry analysis in the studies [25,26].…”