Analytical wave solutions of the (2+1)‐dimensional Boiti–Leon–Pempinelli and Boiti–Leon–Manna–Pempinelli equations by mathematical methods

Abstract

In this manuscript, with the successfully implementation of three mathematical methods, several types of exact and solitary wave solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) and (2+1)-dimensional of Boiti-Leon-Manna-Pempinelli (BLMP) equations are constructed. These schemes, namely called modified extended auxiliary mapping method, ameliorated form of simple equation and modified F-expansion. By transmission, the diverse values to the parameters, variants wave results are derived from exact peregrinating wave solution. Some solutions have been exemplified by graphical to understand the physical deportment of the BLP and BLMP wave models. The accomplished solutions seem with all essential constraint conditions, which are obligatory for them to subsist. Hence, our techniques via fortification of symbolic computations provide an active and potent mathematical implement for solving diverse benevolent nonlinear wave quandaries.

Multi-lump, resonant Y-shape soliton, complex multi kink solitons and the solitary wave solutions to the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for incompressible fluid

“…In [34], the Wronskian determinant solutions are presented. In [35], different wave structures are probed by the simple equation approach. In [36], the higher-order breathers, higher-order lumps and their interactions are considered.…”

Insight into Functional Boiti–Leon–Mana–Pempinelli Equation and Error Control: Approximate Similarity Solutions

“…In [22], a Bäcklund transformation of 2D-BLMPE was constructed by the modified Clarkson-Kruskal direct method. Three mathematical methods were used to construct solitary wave solutions of the 2D-BLPE and 2D-BLMPE [23]. In [24], a special transformation for the N-soliton solution of the 2D-BLMPE was introduced to derive solutions in the long-wave limit.…”

On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid

“…As a result, a lot of authors have studied different analytical solutions to Equation (1) with γ = 0, including the extended tanh function [22], the Bäcklund transformation method [23], the modified exponential function [24], the auxiliary equation method [25], Hirota's direct method [26], ansatz functions and bilinear form [27], (G /G)-expansion [28], He's semi-inverse method [29], the general bilinear form [30], and the modified hyperbolic tangent function [31]. Moreover, the analytical solutions of the (2+1)-dimensional BLMP equation were acquired in works [32][33][34][35] and the integrability of the (2+1)-dimensional BLMP equation was proved in [36]. Meanwhile, the stochastic solutions to Equation (1) have not addressed until now.…”