A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method

New rogon waves for the nonautonomous variable coefficients Schrö dinger equation

“…Recently, many new methods have been constructed to obtain new solutions for nonlinear partial differential equations like symmetry groups, tanh method, trial equation method, sin-Gordon equation method, etc. (Chen et al 2019(Chen et al , 2020Hua et al 2019;Liu et al 2019;Mao et al 2019;Xia et al 2020;Xu et al 2020) (El-Sayed et al 2015, 2014, 2021, 2018aEl-Shiekh and Rehab 2018b;El-Shiekh 2017, 2015, 2013El-Shiekh and Gaballah 2020b;Moatimid et al 2013;Moussa et al 2012;El-Shiekh 2010, 2011;Moatimid and El Shikh 2008;Moussa and El Shikh 2006;Chen et al 2021;He et al 2021;Lü and Ma 2016;Xia et al 2020;Yin et al 2020).…”

Novel solitons and periodic wave solutions for Davey–Stewartson system with variable coefficients

“…Therefore, many new methodologies, for example, tanh method, direct algebric method, Darboux transformation, Painlevé test, integral methods, Bä cklund transformation, trail equation method, etc [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], are constructed for obtaining solitary and soliton wave solutions to nonlinear partial differential equations (NPDEs), but symmetry methods are still the most important techniques in construction and exploitation of nature laws for NPDEs [27][28][29][30][31][32][33]. Many modifications and generalizations are made for symmetry to deal with different types of NPDEs.…”

New Approach of MHD Boundary Layer Flow Towards a Porous Stretching Sheet via Symmetry Analysis and the Generalized Exp-Function Method

“…In the last century, the application of the Lie groups has been developed by a number of mathematicians. Ovsiannikov [1], Olver [2], Ibragimov [3], and Bluman and Kumei [4] are some of the mathematicians who have huge number of studies in that field [5][6][7][8][9].…”