Dynamics of Lump Solutions, Rogue Wave Solutions and Traveling Wave Solutions for a (3 + 1)-Dimensional VC-BKP Equation

Abstract

The (3 + 1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation is studied by using the Hirota bilinear method and the graphical representations of the solutions. Breather, lump and rogue wave solutions are obtained and the influence of the parameter choice is analysed. Dynamical behavior of periodic solutions is visually shown in different planes. The rogue waves are determined and localised in time by a long wave limit of a breather with indefinitely large periods. In three dimensions the breathers have different dynamics in different planes. The traveling wave solutions are constructed by the Bäcklund transformation. The traveling wave method is used in construction of exact bright-dark soliton solutions represented by hyperbolic secant and tangent functions. The corresponding 3D figures show various properties of the solutions. The results can be used to demonstrate the interactions of shallow water waves and the ship traffic on the surface.

Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System

“…Based on that, there are so many important results obtained by considering the classic NLS equation [32], discrete NLS equation [35], the DS equation [33,34,39,42], the Mel'nikov equation [26,29], the Boussinesq-Burgers system [27], the long-wave-short-wave resonance system [8][9][10], and multi-component modified KP hierarchy [11,24,25]. In addition, our team has reported some important work [12,21,36,43,[45][46][47]. Since Feng et al used the KP reduction method to study the nonlocal NLS equations, the study on KP reduction of the nonlocal equations has attracted more and more attention [13].…”

Closed Form Solutions of the Perturbed GerdjikovIvanov Equation With Variable Coefficients

“…4a 2 1 (t)A(t)β(t)γ(t) + 4a 0 (t)a 1 (t)A(t)γ 2 (t) + 16a 0 (t)a 3 1 (t)B(t) + 4a 3 1 (t)C(t) − 4a 3 1 (t)δ(t) = 0, 3a 2 1 (t)A(t)γ 2 (t) + 4a 4 1 (t)B(t) = 0, 4α(t)a 1 (t)a 0 (t)A(t)γ(t) + 2a 1 (t)a 0 (t)A(t)β 2 (t)…”

Novel Rogue Waves for a Mixed Coupled Nonlinear Schrödinger Equation on Darboux-Dressing Transformation

“…The rogue waves attracted a great attention in recent years -cf. [6,7,10,31,34,35], and it is worth noting their close connection to NLS and coupled nonlinear Schrödinger equation(CNLS), Li et al [13] determined reduced and non-reduced vector rogue wave solutions of CNLS using the generalised Darboux transformation (DT), Feng et al [8] employed DT in order to construct multi-breather solutions of NLS on the background of elliptic functions and expressed them via theta functions, Zhang et al [33] used DT in new localised wave solutions; and so on.…”