Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

New Bright and Kink Soliton Solutions for Fractional Complex Ginzburg–Landau Equation with Non-Local Nonlinearity Term

“…We have classified the gained equilibrium point E * of the system (17) using the planar dynamic system theory as follows: if J > 0, then the point is center. The point is said to be saddle if J < 0 and the point is cusp if J = 0, provided the poincare index of the equilibrium point is zero [44,45], see also [29][30][31][32][33][34][46][47][48] for further details. The phase portrait for the system ( 17) is shown in Figures 1-4.…”

“…The complex-valued function ψ = ψ(t, x) constitutes the wave profile, while ψ * (t, x) is assigned to its conjugate. However, the novelty of this paper is to investigate bright and kink soliton solutions using the ansatz method for the governing model (1) and study its dynamic behavior using the theory of the dynamic planner system [27][28][29][30][31][32][33][34]. In this paper, the ansatz method is utilized for the first time to establish wave solutions for the fractional complex Ginzburg-Landau equation with non-local nonlinearity term.…”

Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model

“…Similarly, the dynamics of nonlinear waves on controllable backgrounds due to non-autonomous nonlinearities are explored in Bose-Einstein condensates too [6,[48][49][50][51][52]. Recently, some studies are reported for nonlinear wave structures in certain higher-dimensional nonlinear models describing shallow or deep water waves, which include the analyses of breathers in a variable-coefficient (3+1)D shallow water wave model [53,54], rogue waves and solitons on spatio-temporally variable backgrounds in (3+1)D Kadomtsev-Petviashvili-Boussinesq system [55], solitons in an extended (3+1)D shallow water wave equation [56], and interaction waves in both (3+1)D and (4+1)D Boiti-Leon-Manna-Pempinelli models [57,58] to name a few.…”

Painlev\'{e} integrability, B\"{a}cklund transformations and Wronskian solutions for a (2+1)-dimensional combined potential Kadomtsev-Petviashvili-B-type Kadomtsev-Petviashvili equation in fluid mechanics and plasma physics

“…Plasma physics has been viewed as matter in its plasma phase, while plasmas have been considered as by far the most common phase of ordinary matter in the Universe, both in terms of mass and volume [5][6][7][8]. In order to investigate certain phenomena in plasmas physics, fluid mechanics and other fields, nonlinear evolution equations (NLEEs) have been constructed [9][10][11][12][13][14].…”

“…[10] has derived a two-dimensional generalization of the KdV equation which is called the Kadomtsev-Petviashvili (KP) equation. Recently, researchers have focused their attention on some KP-type equations in fluid mechanics, plasma physics and other fields [11][12][13][14]. A (2+1)-dimensional combined potential KP-B-type KP (pKP-BKP) equation has been constructed in fluid mechanics and plasma physics [15][16][17][18][19],…”