Abundant lump solutions and interaction solutions of a (3+1)-D Kadomtsev-Petviashvili equation

Abstract

In this paper, abundant lump solutions and two types of interaction solutions of the (3+1)-D Kadomtsev-Petviashvili equation are obtained by the Hirota bilinear method. Some contour plots with different determinant values are sequentially given to show that the corresponding lump solution tends to zero when the determinant approaches to zero. The interaction solutions with special parameters are plotted to elucidate the solution properties.

Rational Solutions and Their Interaction Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation

“…Remark 1. When choosing N = 2, n i = 1 in expression (4), the rational solution is reduced to the lump solution [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][45][46][47][48][49][50][51][52][53][54][55][56][57].…”

Rational Wave Solutions and Dynamics Properties of the Generalized ( 2 + 1 )-Dimensional Calogero-Bogoyavlenskii-Schiff Equation by Using Bilinear Method

“…By using a transformation of the potential function of NLEEs and the definition and properties of the D operator, NLEEs are written in bilinear form, and then, the single-double-multiple soliton solutions of NLEEs can be obtained by using the small parameter expansion method. Based on these methods, one can try to find many interesting analytical solutions of NLEEs, such as the rogue wave solutions [2][3][4], the multiple wave solutions [5,6], the lump solutions [7][8][9], the periodic wave solutions [10][11][12][13], the Wronskian solutions [14,15], the rational solutions [16,17], the high-order soliton solutions [18,19], the solitary wave solutions [20,21], and the other solutions [22][23][24][25][26][27].…”

Abundant exact analytical solutions and novel interaction phenomena of the generalized (3+1)-dimensional shallow water equation

“…So far, several effective methods have been established by mathematicians and physicists to obtain exact solutions of NLEEs [1][2][3][4][5][6][7][8]. By using these methods, researchers constructed the exact solutions of NLEEs, such as soliton [9], rogue wave [10], breathers [11], periodic wave [12], three-wave solution [13], rational solutions [14], lump solution [15] and interaction solutions [16]- [18], etc.…”

“…In soliton theory, lump solutions have received increasing attention recently [15]. In particular, collisions between lump solutions and other forms of soliton solutions have been studied [16]- [18].…”