Painlevé analysis, Lie symmetries and exact solutions for (2+1)-dimensional variable coefficients Broer–Kaup equations

Lie symmetry analysis, nonlinear self-adjointness and conservation laws to an extended (2+1)-dimensional Zakharov–Kuznetsov–Burgers equation

“…Due to the increased interest in the NLEEs, a broad range of analytical and numerical methods have been developed to construct exact solutions to NLEEs. Some of these efficient methods are the Lie symmetry method [1][2][3], Darboux transformation method [4], Jacobi elliptic method [5], Painleve analysis [6], the inverse scattering method [7], the Baklund transformation method [8], the conservation law method [9], the Hirota bilinear method [10], the ansatz method [11] and many other methods.…”

Solutions of Konopelchenko-Dubrovsky Equation by Traveling Wave Hypothesis and Lie Symmetry Approach

“…In this subsection, we apply Lie symmetry approach [11,12] to find symmetries and we obtain some exact solutions of equations (1) and (2).…”

New dynamical behavior of two waves for (2+1)-dimensional Broer-Kaup equation

“…By means of the homogeneous balance method [8, 16-19, 21, 24] solitary wave solutions, exact multi-soliton solutions and soliton-like solutions of the BK equation were obtained. Meanwhile, doubly periodic wave solutions, folded solitary wave solutions, non-Lie symmetry groups and new exact solutions were derived [6] by using variable separation approach [1,3,11,12,15,22], Painleve analysis method [5,20] and generalized Riccati mapping method [10,23]. In this work, we consider the following (2 + 1)D BK Equation:…”

“…The (2 + 1)-dimensional Broer-Kaup Equation ((2 + 1)D BK for short) comes from the constraints of the KP equation and it is of importance in mathematical physics field. Many researchers pay more and more attention to search for analytical exact solution to (2+1)D BK Equation because of its rich physical connotation [1,[3][4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22][23][24]. By means of the homogeneous balance method [8, 16-19, 21, 24] solitary wave solutions, exact multi-soliton solutions and soliton-like solutions of the BK equation were obtained.…”