The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations

By Abdul-Majid Wazwaz. Applied Mathematics and Computation, 2007

319 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fdd2f50747737c3eb0bb6586b77b56f8c5b067fe

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Citations in the corpus

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation (2009, methodology): “Later it was broadly adopted in the extended tanh-function method [13,14], the tanh–coth method [16], the F-expansion method [19], the mapping method [20,36], and the extended F-expansion method [21,22].”
The modified benjamin-bona-mahony equation via the extended generalized riccati equation mapping method (2012, unknown): “In recent times, many researchers established various methods to construct exact traveling wave solutions of the nonlinear PDEs, such as, the inverse scattereing method [1], the variational iteration method [2,3], the Hirota’s bilinear transformation method [4], the Jacobi elliptic function expansio”
Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations (2020, methodology): “TheNewell-Whitehead equationwhich is also known as Newell–Whitehead–Segel equation explains the dynamical behaviour near the bifurcation point for the Rayleigh-Benard convection of binary fluid mixtures [7].”
New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations (2020, methodology): “In recent years, several efficient methods including method of extended tanh [1, 2], tanh-coth [3, 4], Hirota’s direct [5, 6], sine-cosine [7, 8], extended direct algebraic [9, 10], extended trial approach [11, 12], Exp [-φ(ξ)]-Expansion [13, 14], a new auxiliary equation [15, 16], Jacobi elliptic a”
A multiple exp-function method for nonlinear differential equations and its application (2010, methodology): “ = const.) in [31], and the Kolmogorov-Petrovskii-Piskunov equation through a ﬁrst-order ordinary diﬀerential equation η′ = 1 ±η2 in [9]. It has been broadly adopted in the tanh-function type methods [10, 11, 14], the Jacobi elliptic function method [32, 33], 3 the mapping method [34, 35], the F-exp”
Haar wavelet method for solving some nonlinear Parabolic equations (2010, methodology): “A variety of powerful methods, such as inverse scattering method [3], bilinear transformation [4], Backland transformation, a bilinear form [4], the tanh-sech method [5–7], extended tanh method [6], sine-cosine method [8], homogeneous balance method [9], Exp-function method [10], the tanh method [11”
Polynomial differential quadrature method for numerical solutions of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients (2014, unknown): “In this example, we consider the nonlinear standard Fitzhugh– Nagumo partial differential equation [15,44] ut 1⁄4 uxx uð1 uÞðq uÞ 1⁄4 0; ðx; tÞ 2 1⁄2A;B 1⁄20;T ; ð5:2Þ”