Abundant analytical soliton solutions and Evolutionary behaviors of various wave profiles to the Chaffee–Infante equation with gas diffusion in a homogeneous medium

New Exact Solutions of Landau-Ginzburg-Higgs Equation Using Power Index Method

“…[1]. Recently, several methods have been used to find exact solutions of nonlinear model equations like Cahn-Allen equation [2], ð2 + 1Þ -dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation [3], Newell-Whitehead-Segel (NWS) equations [4], the Chaffee-Infante equation [5], DNA Peyrard-Bishop equation [6], Burger's equation [7], the ð2 + 1Þ-dimensional nonlinear Sharma-Tasso-Olver equation [8], and Ablowitz-Kaup-Newell-Segur water wave equation [9]. Recently, a number of concrete techniques have been recognized for finding accurate and comprehensible solutions of nonlinear physical models with the help of computer algebra, such as Maple, MATLAB, and Mathematica.…”

The residual symmetry, Bäcklund transformations, CRE integrability and interaction solutions: (2+1)-dimensional Chaffee–Infante equation

“…Here, bifurcation in a system parameter that indicates the potential's steepness also increases the model's attractiveness [35]. The CI equation has been studied using the modified Khater method [35], Lie symmetry analysis [36], the first integral method [37], and a variety of other approaches [38,39].…”

“…Figure 3. (a) 3D-plot of u 5 (1, y, t) given in equation (39), (b) 2D-plot of u 5 (1, 1, t) given equation (39), (c) 3D-plot of u 5 (x, y, 1) given in equation(39) where s 0 = 1,s 1 = 3, s 2 = 2, r 2 = 2, q 2 = −2, r 1 = 1, q 1 = −1, r 1 = 1, r 2 = 4.5, δ 1 = 1, η 0 = 2, α = 1, σ = 0.5, η 0 = −9, ξ 0 = 0.…”

Extended Calogero-Bogoyavlenskii-Schiff equation and its dynamical behaviors

“…Furthermore, Manakov et al discovered in [9] that the interactions of lump waves do not result in a pattern of phase changes. Regarding that, many powerful methods for finding the lump solutions of NPDEs have been developed over the past decades, including the long-wave limit approach [7,10], the nonlinear superposition formulae [11], the inverse scattering transformation [12,13], the invariance and Lie symmetry analysis [14,15], the Bäklund transformation [16,17], the bilinear neural network method [18][19][20][21][22][23][24], the Darboux transformation [25,26] and the Hirota bilinear method [27][28][29][30][31], Symbolic computation method [32][33][34][35] and other different methods [36][37][38][39][40][41][42][43]. Among the approaches stated above, taking a 'long wave' limit of the corresponding N-soliton solutions plays an important role in the investigation of M-lump solutions for nonlinear partial differential equations.…”