A Wronskian formulation of the (3 + 1)-dimensional generalized BKP equation

Abstract

In this paper, a (3 + 1)-dimensional generalized B-type Kadomtsev–Petviashvili (BKP) equation is mainly discussed. Based on the Wronskian technique, a Wronskian formulation is established. Generating functions for matrix entries satisfy a linear system of partial differential equations involving a free parameter. The resulting solutions formulae provide us with a comprehensive approach to constructing rational solutions, positons and complexitons for the (3 + 1)-dimensional generalized BKP equation.

A KdV-Type Wronskian Formulation to Generalized KP, BKP and Jimbo–Miwa Equations

“…) Similarly, the extended (3+1)-dimensional Jimbo-Miwa equation has a set of sufficient conditions defined by Eq. (15) with…”

New Exact Solutions for the (3+1)-Dimensional Generalized BKP Equation

“…The study of the BKP equation has attracted a considerable size of research work. These equations were studied using the Hirota method, the multiple exp-function algorithm, the Pfaffian technique, Riemann theta functions, the extended homoclinic test approach, and Bäcklund transformation by many authors [17][18][19][20][21][22][23][24][25][26]. In this paper, based on the Wronskian method, the new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions of the (3+1)-dimensional generalized BKP equations are investigated.…”

Bäcklund transformation and shock-wave-type solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid mechanics

“…Nowadays, marine scientists are making use of the KadomtsevPetviashvili (KP)-category equations 1 in such oceanic investigations as those on the soliton turbulence from surface-wave data obtained in the Currituck Sound, North Carolina, and Adriatic Sea (Costa et al, 2014), KP applicability near the Dogger Bank, North Sea (Soomere, 2010), three-dimensional peculiarities of largeamplitude internal waves in the Strait of Gibraltar (Vlasenko et al, 2009), internal waves over the New Jersey's continental shelf (Shroyer et al, 2011), interaction and generation of longcrested internal solitary waves in the South China Sea to explain the satellite image (Chen et al, 2011), speeds of strongly nonlinear near-surface internal waves in the Strait of Georgia (Wang and Pawlowicz, 2011), shallow ocean-wave soliton interactions on flat beaches (Ablowitz and Baldwin, 2012), danger of resonant internal modified-KP solitons for submarines, oil and gas platforms, oil risers and pipelines (Soomere, 2010), wave-making experiments related to the internal solitary waves in the ocean (Huang et al, 2013), force exerted on a cylindrical pile by ocean internal waves derived from nautical X-band radar observations and in-situ buoyancy frequency data (Zha et al, 2012), large and rogue waves in a near-sea-surface layer (Kovalyov, 2014) and soliton dynamics related to seismically generated tsunamis (Arcas and Segur, 2012).…”

“…As a part of the KP-category equations, the (3þ1)-dimensional Btype KP (or BKP) equations 2 have attracted a good size of recent research in fluid mechanics and other fields (Zhang, 2010;Kudryashov, 2010;Asaad and Ma, 2012;Ma and Zhu, 2012;Shen and Tu, 2011;Cheng et al, 2013;Wazwaz, 2011;Abudiab and Khalique, 2013;Bhrawy et al, 2013;Ebadi et al, 2013;Huang et al, 2015). One of them, a (3þ1)-dimensional constant-coefficient BKP equation, has newly been constructed, which can be applied to describe the propagation of nonlinear waves in fluid dynamics, as (Wazwaz, 2012;Abudiab and Khalique, 2013;Huang et al, 2015) …”