Quasi Media Research Articles

Multiple soliton and M-lump waves to a generalized B-type Kadomtsev–Petviashvili equation

In this study, we focus on the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation in fluid dynamics, which is useful for modeling weakly dispersive waves transmitted in quasi media and fluid mechanics. As a general matter, this paper examines the gBKP equation including variable coefficients of time that are widely employed in plasma physics, marine engineering, ocean physics, and nonlinear sciences to explain shallow water waves. Using Hirota’s bilinear approach, one-, two, and three-soliton solutions to the problem are constructed. By employing a long-wave method, 1-M-, 2-M, and 3-M-lump solutions are derived. In addition, interaction phenomena of one-, and two-soliton solutions with one-M-lump wave are revealed. Moreover, an interaction solution between a two-M-lump wave and a one-soliton solution is also offered. The planes that M-lump waves travel among them are derived. We believe that our findings will help improve the dynamical properties of (3+1)-dimensional BKP-type equation.

Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Soliton molecules may exists in both experimental and theotetical aspects. In this work, we investigate the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation, which can be used to describe weakly dispersive waves propagating in the quasi media and fluid mechanics. Soliton molecules are generated by N-soliton solution and a new velocity resonance condition. Furthermore, soliton molecules can become to asymmetric solitons when the distance between two solitons of the molecule is small enough. Based on the N-soliton solution, we obtain some novel interaction solutions which component of soliton molecules, breather waves and lump waves by deal with part of parameters by applying velocity resonance, module resonance and long wave limit method, and the interactions are elastic. Finally, some graphic analysis are discussed to understand the propagation phenomena of these solutions.

Analysis on lump, lumpoff and rogue waves with predictability to the (2 + 1)-dimensional B-type Kadomtsev–Petviashvili equation

In this work, we investigate the (2+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation, which can be used to describe weakly dispersive waves propagating in the quasi media and fluid mechanics. We construct the more general lump solutions, localized in all directions in space, with more arbitrary autocephalous parameters. By considering a stripe soliton generated completely by lump solution, a lumpoff solution is presented. Its lump part is cut by soliton part before or after a specific time, with a specific divergence relationship. Furthermore, combining a pair of stripe solitons, we obtain the special rogue waves when lump solution is cut by double solitons. Our results show that the emerging time and place of the rogue waves can be caught through tracking the moving path of lump solution, and confirming when and where it happens a collision with the visible soliton. Finally, some graphic analysis are discussed to understand the propagation phenomena of these solutions.

On periodic wave solutions with asymptotic behaviors to a [formula omitted]-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid dynamics

In this paper, a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation is investigated, which can be used to describe weakly dispersive waves propagating in a quasi media and fluid mechanics. Based on the Bell polynomials, its multiple-soliton solutions and the bilinear form with some reductions are derived, respectively. Furthermore, by using Riemann theta function, we construct one- and two-periodic wave solutions for the equation. Finally, we study the asymptotic behavior of the periodic wave solutions, which implies that the periodic wave solutions can be degenerated to the soliton solutions under a small amplitude limit.