Multiple wave solutions and auto-Bäcklund transformation for the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation

Abstract

a b s t r a c tThe multiple Exp-function method is used to construct multiple wave solutions to the (3 + 1)-dimensional generalized BKP equation. The resulting solutions involve generic phase shifts and wave frequencies containing some existing choices. By taking the standard truncated Painlevé analysis, we obtained an auto-Bäcklund transformation and some types of exact solutions of the (3 + 1)-dimensional generalized BKP equation. Moreover, the linear superposition principles of hyperbolic and trigonometric function solutions are also presented.

Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation

“…Balancing the linear term of the highest order with the highest order nonlinear term, we can easily obtain n � 1 and thus (20) becomes…”

“…Soliton solutions in Wronskian form of (1) were also presented in [18,19]. Multiple wave solutions and auto-Bäcklund transformation for the (1) were obtained in [20]. e lump solutions, periodic waves, and rogue waves as well as interaction solutions of (1) were obtained in [21].…”

“…e study of different BKP equations has attracted a considerable size of research. Different forms of BKP equations were studied by using the Hirota method, the multiple exp-function algorithm, the Pfaffian technique, the Wronskian technique, and the Bäcklund transformation [15][16][17][18][19][20][21]. In this paper, by means of the Lie symmetry group method, we consider the following (3 + 1)-dimensional generalized BKP equation:…”

Two New Modifications of the Exp-Function Method for Solving the Fractional-Order Hirota-Satsuma Coupled KdV

“…And in the meantime, obtaining the exact soliton solutions to these equations is more important because this study gives us a great deal of information on various sciences such as fluid mechanics, physics, and mathematics. So, a lot of research has begun in recent years to get this style of solutions [34][35][36][37][38][39][40][41][42][43][44]. This concept was first introduced by John Scott Russell (1818-1388).…”

N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation

“…The B-type Kadomtsev-Petviashvili (KP) equations are considered as non-linear models in the fluids or the plasmas which have been investigated using different methods [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. In this paper, a B-type KP equation with certain applications in the fluids is studied such that its mathematical model can be expressed [36,37]:…”