On the solution of certain higher-order local and nonlocal nonlinear equations in optical fibers using Kudryashov's approach

Some exact wave solutions of nonlinear partial differential equations by means of comparison with certain standard ordinary differential equations

“…In parallel with these methods, efforts have also gone into the development of simpler techniques for the derivation of explicit particular solutions of nonlinear evolution equations which may be handled by symbolic computational techniques. [23][24][25] These include the G ′ ∕G-method, the tanh-function, and Exponential function methods. [26][27][28] In this connection, a significant development was the introduction of a new method by Kudryashov 29 which subsumed in a sense the various methods mentioned above.…”

“…The inverse scattering transform, Hirota bilinearization method, Darboux transformations, Lie symmetries, and Painlevé analysis 14–22 are extremely powerful tools for the analysis of integrable systems. In parallel with these methods, efforts have also gone into the development of simpler techniques for the derivation of explicit particular solutions of nonlinear evolution equations which may be handled by symbolic computational techniques 23–25 . These include the $$$ {G}^{\prime }/G $$$‐method, the $$$ \mathit{\tanh} $$$‐function, and Exponential function methods 26–28 .…”

Microdynamic and thermodynamic properties of dissipative dust-acoustic solitons

“…Solitons were first discovered on the water surface by Russell in 1838 [2]. Subsequently, solitons were discovered in plasma, waveguides, and electrical circuits and acquired the status of fundamental objects of nonlinear wave physics, new properties of which are being discovered up to the present day [3][4][5][6][7]. The concept of dissipative solitons is a new paradigm in the physics of nonlinear waves [8].…”

On the Exact Solitary Wave Solutions to the New ( 2 + 1 ) and ( 3 + 1 )-Dimensional Extensions of the Benjamin-Ono Equations

“…(3), to employ the Kudryashov method [13,14] as a powerful integration method for treating various nonlinear evolution equations (see also [15][16][17][18][19][20][21][22][23] for other methods). The Kudryashov method and its modified versions have been investigated by capable authors in the plenty of nonlinear models such as the nonlinear differential equations [24], higher-order local and nonlocal nonlinear equations in optical fibers [25], some (2 + 1)-dimensional nonlinear evolution equations [26], exact traveling wave solutions of the PHI-four equation, and the Fisher equation [27]. As we all know, some novel and important developments for searching the analytical solitary wave solutions for PDE were investigated.…”