The modified extended tanh-function method for solving Burgers-type equations

By Abdel-Maksoud Abdel-Kader Soliman. 2006

190 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/213ef31bc69dc64ba558697ebf3f0d6b2622f52d

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In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

A differential quadrature method for numerical solutions of Burgers'‐type equations (2012, methodology): “Again, the system of ODEs (24)-(26) is solved by Runge-Kutta fourth order method (Soliman, 2006).”
Mathematical studies of the solution of Burgers' equations by Adomian decomposition method (2019, methodology): “3 Test case 3 This test case was also presented in Wazwaz25 Further, this homogeneous viscous Burgers' equation (29) has the initial condition u(x, 0) = 2 sin x cos x + 1 ≡ g(x).”
New class of solutions for water infiltration problems in unsaturated soils (2010, methodology): “A tangent-hyperbolic function is commonly applied to solve these transform equations (Abdou and Soliman 2006, Soliman 2006).”
Expanding the Tanh-Function Method for Solving Nonlinear Equations (2011, methodology): “function method in the form [13] values of .”
A Chebyshev spectral collocation method for solving Burgers'-type equations (2008, methodology): “Consider a 1D Burgers’ equation: ut + αuux − νuxx = 0, x ∈ Dx[0, T ], (49) with the solitary wave solutions [41], u(x, t) = c/α + (2ν/α)tanh(x − ct), (50) in the region D = {x : a < x < b}; α and ν are arbitrary constants.”
Exact solutions of some nonlinear systems of partial differential equations by using the first integral method (2012, methodology): “In recent years, many approaches to nonlinear systems of PDEs have been employed, such as the extended tanh function method [1–4], the modified extended tanh function method [5,6], the exp-function method [7–9], the Weierstrass elliptic function method [10] and the first integral method [11].”