Evolutionary behavior of rational wave solutions to the (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abstract

A nonlinear integrable model known as the (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (4D-BLMP) equation is studied in the present paper. To this end, by considering the Hirota bilinear form of the model and utilizing the linear superposition method (LSM) along with symbolic computations, a group of rational wave solutions including multiple wave and positive (non-singular) compelexiton solutions is formally derived. The dynamical behavior of the solutions is also analyzed graphically by considering the special values of the involved parameters. The results of the current work reveal the existence of different wave structures to the 4D-BLMP equation and distinguish it from other models that do not possess non-singular compelexiton solutions.

Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type system

“…Nonlinear partial differential equations (NLPDEs) have rapidly become indispensable in the quest to conceptualise the world around us [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] . We give a few recent studies of NLPDEs presented in the literature.…”

“…The authors of [6] examined the KP-BBM equation and constructed periodic, multi wave, cross-kink wave and breather wave solutions. The (4 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation was studied using the Hirota bilinear form and rational wave solutions were obtained in [7] . Lie symmetry analysis was carried out on a generalized (2 + 1)-dimensional KP equation [8] and in [9] , the (2 + 1)-dimensional dispersive long wave equation was investigated via the truncated Painlevé series method.…”

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

“…As an extended shallow water wave model in the higher dimensions, the Boiti-Leon-Manna-Pempinelli (BLMP) equation has been considered for the wave motion in an incompressible fluid [57,58]. Because the higher-dimensional models allow more abundant analytic solutions than the lower-dimensional models, researchers have paid attention to the higherdimensional BLMP equations [59][60][61][62][63].…”

“…with G(x, y, z, t) being a differentiable function with respect to x, y, z and t, H (x , y , z , t ) being a differentiable function of the independent variables x , y , z and t , while a 1 , a 2 , a 3 and a 4 being the non-negative integers. Reference [62] has also obtained the N -soliton solutions for Eqn. (2) as…”

Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

“…Nonlinear PDEs appear in condensed matter, solid state physics, fluid mechanics, chemical kinetics, plasma physics, nonlinear optics, propagation of fluxion in Josephson junctions, ocean dynamics and many others [18][19][20][21][22][23][24][25][26][27]. In order to understand the different nonlinear phenomena, various methods for obtaining exact solutions to nonlinear PDEs have been proposed [28][29][30][31].…”