Some singular solutions and their limit forms for generalized Calogero–Bogoyavlenskii–Schiff equation

Folded novel accurate analytical and semi-analytical solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation

“…Another goal of the manuscript is to limit the examination of the semi-analytical and numerical solutions of the considered model to an explanation of the accuracy of the analytical solutions obtained and the analytical schemes used [23,24]. The generalized CBS equation is given by [25][26][27][28][29][30]:…”

Traveling Wave Solutions of the Extended Calogero-Bogoyavlenskii-Schiff Equation

“…(1) Where u(x, y, t) is a function of space variables x, y and temporal variable t. Equation ( 1) is also obtained by unifying two directional generalization of the potential KdV equation and Calogero-Bogoyavlenskii-Shiff equation [26][27][28]. The explicit N-soliton solutions of equation ( 1) is obtained in [25].…”

Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)-Expansion Method

“…These solutions will play an important role in soliton theory. In order to get exact solutions directly, many powerful methods have been introduced such as inverse scattering method [1], bilinear transformation [2], Bäklund and Darboux transformation [3][4][5], tanh-sech method [6,7], extended tanh method [8], Exp-function method [9][10][11], the sine-cosine method [12][13][14], the Jacobi elliptic function method [15], -expansion method [16,17], auxiliary equation method [18,19], bifurcation method [20][21][22], homotopy perturbation method [23], and homogeneous balance method [24,25]. Recently, Wang et al [26] introduced a new approach, namely, the ( / )-expansion method, for a reliable treatment of the nonlinear wave equations.…”