Rational solutions and their interaction solutions for the (2+1)-dimensional dispersive long wave equation

Abstract

The Hirota bilinear form of the (2+1)-dimensional dispersive long wave equation by the truncated painlevé series in this paper is obtained. Meanwhile, a pair of quartic-linear forms are also constructed by an appropriate selection of seed solution to explore the lump solutions of the (2+1)-dimensional dispersive long wave equation. Then some novel interaction solutions by combining quadratic functions and exponential functions are yielded. Finally, in order to better illustrate the features of the results, we draw the three-dimensional and two-dimensional figures.

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 (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. A new method was introduced in [10] to find exact solutions for NLPDEs of mathematical physics.…”

Diverse exact analytical solutions and novel interaction solutions for the (2+1)-dimensional Ito equation

“…Moreover, this method had a profound impact on both pure and applied areas of mathematics, physics, and mechanics, etc. Based on these methods, researchers generated various numerical solutions and exact solutions which contained rogue wave [20], rational solution [21], soliton solution [22], lump solution which localized in all directions of the space [23], periodic solution [24], etc. Hitherto, as per Hirota bilinear method and symbolic computation, we derived various exact solutions of NLEEs [25][26][27][28][29][30].…”