New Exact Solutions of some (2 + 1)-Dimensional Nonlinear Evolution Equations Via Extended Kudryashov Method

Exact Solutions to a Class of Schamel Nonlinear Equations Modeling Dust Ion-acoustic Waves in Plasma

“…In this section, we summarize the essential steps of the extended Kudryashov method [24,25] in the following steps:…”

“…The Kudryashov method was presented by Kudryashov [18]- [20] and it has been applied by many authors [21]- [23]. The extended Kudryashov method [24,25] is direct effective and provides more new exact solutions by taking the combination of all solutions of the Bernoulli and Riccati equations.…”

Conservation Laws and Travelling Wave Solutions for System of Ion Sound and Langmuir Waves

“…The investigation of the exact solutions of NLEEs are important to provide better information, know the mechanism and their applications. With the aid of symbolic computation software such as Mathematica or Maple abundant methods are extensively studied to obtain exact solutions, for example the Bäcklund transform [1,2], the extended tanh-function method [3], the F-expansion method [4], sine-cosine method [5], the extended F-expansion method [6], Jacobi elliptic function method [7], the Kudryashov method [8], the extended Kudryashov method [9,10], the lie point symmetry method [11]- [13] and other methods [14]- [17]. The dynamical behavior for a famous class of NLEEs is presented in [18].…”

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.…”