Exact Solutions to a Generalized Bogoyavlensky‐Konopelchenko Equation via Maple Symbolic Computations

Abstract

We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are made for solving both the nonlinear equation and the corresponding bilinear equation. A few classes of exact and explicit solutions are generated from different ansätze on solution forms, including traveling wave solutions, two-wave solutions, and polynomial solutions.

Searching for Analytical Solutions of the (2+1)‐Dimensional KP Equation by Two Different Systematic Methods

“…For instance, the singular behaviors [12,13] and impulsive phenomena [14,15] often show some blow-up properties [16,17] which happen in lots of complex physical processes. In order to solve various differential equations, some analytical tools as well as symbolic calculation techniques were established, such as fixed-point theorems [18,19], variational methods [20,21], topological degree method [22][23][24][25], iterative techniques [26,27], bilinear method [28][29][30][31], modified simple equation method [32], exp(− ( ))-expansion method [33][34][35][36][37][38], Lie group method [39,40], and complex method [41][42][43][44][45][46][47][48][49][50].…”

Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena

“…Besides, the authors in [23] applied the Lie symmetry method to (1.2) and investigated its conservation laws. Some lump solutions and interacted soliton solutions had been obtained using the Hirota bilinear method in [5,6,8,11,12,14,18]. On the other hand, some authors studied the variable-coefficient Bogoyavlensky-Konopelchenko (VCBK) equation…”

Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation

“…Moreover, Eq. (0.2) is considered as Bogoyavlensky-Konopelchenko (BK) equation [28] , [29] by below form The generalized BK equation [30] is given as below in which , and , and are specified values. Eq.…”