On solutions of the Newell–Whitehead–Segel equation and Zeldovich equation

Abstract

In this study, we present new solutions of Newel-Whitehead-Segel and Zeldovich equations via the new extended direct algebraic method (EDAM) by taking the special values to involved parameters in the method. The novel exact and soliton solutions are extracted in form of generalized trigonometric and hyperbolic functions. These acquired results reveal the supremacy of the new EDAM. For more illustration of our retrieved solutions, some distinct kinds of 2D and 3D graphs are presented.

A view of solitary wave solutions to the fractional DNA Peyrard-Bishop equation via a new approach

“…Many researchers have thoroughly examined nonlinear partial differential equations (PDEs), and numerous techniques have been devised to address these PDEs. To obtain exact solutions to the nonlinear PDEs, various effective mathematical approaches have been utilized in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Construction of optical solitons of magneto-optic waveguides with anti-cubic law nonlinearity

“…2014 ; Haider 2017 ; Hasegawa and Miyazaki 1992 ; Raza and Arshed 2020 ; Rehman et al. 2021a ; b ; c ; Khan 2020 ; Kudryashov 2019 ; Qiu et al. 2019 ; Shoji and Mizumoto 2018 ; Wazwaz 2008 ; Yan et al.…”

Investigation of numerical solutions of fractional generalized reguralized long wave equations by least squares-residual power series method

“…Methods such as the sine-cosine method [13], (G′/G)-expansion method [14], extended direct algebraic method [15], and residual power series method [16][17][18][19] are used when searching for solutions of FDEs. In addition to these, there are different methods that can be adapted to fractional differential equations [20][21][22].…”