Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the $$(2+1)$$-dimensional KP-BBM equation

A new implementation of a novel analytical method for finding the analytical solutions of the (2+1)-dimensional KP-BBM equation

“…They have demonstrated the effectiveness of the proposed technique and described the physical interpretation of the nonlinear processes. Kumar et al [41] obtained the abundant wave solutions to the (2+1)-dimensional KP-BBM equation via two powerful methods.…”

Non‐classical Lie symmetries for nonlinear time‐fractional Heisenberg equations

“…These transformations play an essential role in the analysis of different types of differential equations. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] Fractional calculus, that dating back to 1695, 15 has made remarkable progress in recent decades. There is a fundamental difference between right-order differential operators and Riemann-Liouville fractional derivatives, the former being local operators, the latter not.…”

“…As we know, Lie group transformations were first proposed in the early nineteenth century by the Norwegian mathematician Sophos Lee. These transformations play an essential role in the analysis of different types of differential equations 1–14 . Fractional calculus, that dating back to 1695, 15 has made remarkable progress in recent decades.…”

Exact closed-form solutions and dynamics of solitons for a $$(2+1)$$-dimensional universal hierarchy equation via Lie approach

“…The exact analytical solutions provide much more specific information of the complex physical problems describing such types of NPDEs. Over the last five decades, some methods have been developed successfully to obtain soliton and group-invariant solutions of NPDEs for their trustworthy processes like as tanh function method [1], notably first integral technique [2], F-expansion technique [3], Painlevé analysis [4], cosh-sinh method and tanh-sech technique [5], expfunction method [5][6][7], extended F-expansion technique [8,9], extended homotopy perturbation method [10], Riccati equation rational expansion method [11], symmetry reductions of the Lax pair [12], Bäcklund transformation [13], general direct method [14], Hirota's bilinear method [15] and Lie symmetry method [16][17][18][19][20][21][22][23][24][25][26].…”