The improved <i>F</i>-expansion method and its application to the MEE circular rod equation and the ZKBBM equation

Islam, Md. Shafiqul; Akbar, M. Ali; Khan, Kamruzzaman

doi:10.1080/23311835.2017.1378530

Cited by 16 publications

(1 citation statement)

References 26 publications

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“…Several researchers and mathematicians have paid much attention to obtaining exact rational solutions and closed-form solutions of numerous nonlinear models of NLEE. In the process of doing so, various powerful and efficient analytical mathematical methods have been developed for finding exact analytical solutions, for example, the Bäcklund transformation method [1], the Darboux transformations method [2], the inverse-scattering method [3], the Hirota bilinear method [4], the auxiliary equation method [5], the exp-function method [6], the Lie symmetry method [7][8][9][10][11], the modified F-expansion method [12], modified simple equation methods [13], the ¢ G G ( ) -expansion method [14,15], the generalized exponential rational function method [16,17], and so on. Closed-form solutions of NLEEs play a significant role in our understanding of the dynamical structures and characteristic properties of various nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

Kumar¹,

Niwas²,

Osman³

et al. 2021

Commun. Theor. Phys.

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The prime objective of this paper is to explore the new exact soliton solutions to the higherdimensional nonlinear Fokas equation and (2+1)-dimensional breaking soliton equations via a generalized exponential rational function (GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons, double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons, elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.

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