Symmetries, reductions and exact solutions of Broer-Kau-Kupershmidt system

Abstract

In this paper, using the modified Clarkson-Kruskal direct method, the symmetries and the reductions of (2+1) dimensional Broer-Kau-Kupe-rshmidt (BKK) are obtained. At the same time, a great many of solutions are derived by solving the reduction equations, including the rational functions hyperbolic functions, the trigonometric functions, the power series solution, and the Airy function solution.

Homotopic mapping solitary traveling wave solutions for the disturbed BKK mechanism physical model

“…Then from Eq. ( 5), we can obtain the reduced equations of the typical BKK mechanism system (3) and (4) as follows: [17] θ τξ + 2θ ξ ξ − θ τττ + 2θ 2 ξ + 2θ θ ξ ξ − 2ω ξ ξ = 0, ( 6)…”

“…From Eqs. ( 6) and (7), using the G/G developed method and the auxiliary function Riccati developed method, we can obtain the following solitary solution Ū, V of the typical BKK mechanism model ( 3) and (4) (as λ 2 − 4µ > 0): [17] Ũ(t, x, y)…”

Exact solutions of the nonlinear differential—difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete (G′/G)-expansion method

“…These are probably the reasons why, since pioneering works by Hirota and Suzuki [6] on electrical transmission lines simulating Toda lattice, a growing interest has been devoted to the use of nonlinear transmission lines, in particular, for studying nonlinear waves and nonlinear modulated waves: pulse solitons, envelope pulse (bright), hole (dark) solitons and kink and anti-kink solitons, [7][8][9] intrinsic localized modes (also called discrete breathers), [10][11][12] modulational instability. [13][14][15][16][17] Several methods for finding the exact solutions of nonlinear evolution equations for mathematical physics have been proposed, [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] such as Jacobian elliptic function method, [35,36] Fibonacci tanh function for NDDEs, [37] Expfunction method, [38,39] variable-coefficient discrete (G /G)expansion method for NDDEs, [40] and so on. In order to establish the effectiveness and reliability of the (G /G)-expansion method and to expand the possibility of its application, further research has been carried out by a considerable number of researchers.…”