The Mathematica implementation of the tanh and sech-methods for computing exact travelling wave solutions of nonlinear partial differential equations (PDEs) is presented. These methods also apply to ordinary differential equations (ODEs). New algorithms are given to compute polynomial solutions of ODEs and PDEs in terms of the Jacobi elliptic functions. An adaptation of the tanh-method to nonli...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

The model for α = 1, β = 1/(m + 1) and γ = 0 was studied by Bagolubasky and Clarkson et al. A second model for α = 0, β = −(1/2) and γ = 0 was studied by Parker and solitary wave solutions were obtained as well. However, a third model was investigated in Refs. 10 and 11 for m = 1 and m = 2 where explicit solitary wave solutions and kinks solutions were derived. For m ≥ 1, we get consecutive exp...

The task scheduling problem in heterogeneous system is known as NP-hard. Recently, Bajaj and Agrawal proposed an algorithm TANH (Task duplication-based scheduling Algorithm for Network of Heterogeneous systems) with optimality conditions, which are wider than previous optimality conditions. TANH algorithm combines the clustering technique with task duplication. We propose two postprocessing alg...

In [5] and [2] the authors describe the remarkable effectiveness of the doubly exponential ‘tanh-sinh’ transformation for numerical integration —even for quite unruly integrands. Our intention in this note is to provide a theoretical underpinning when the integrand is analytic for the observed superlinear convergence of the method. Our analysis rests on the corresponding but somewhat easier ana...

Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count Data We develop a robust estimator—the hyperbolic tangent (tanh) estimator—for overdispersed multinomial regression models of count data. The tanh estimator provides accurate estimates and reliable inferences even when the specified model is not good for as much as half of the data. Seriously ill-fitted counts...

An application of the generalized tanh–coth method to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for variants of the KdV–Burger and the K(n, n)–Burger equations. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exac...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

Abstract In this study, we present two different methods a sech-tanh method and extended tanh-method to obtained the soliton solutions of the two-dimensional Korteweg-de Vries-Burgers (KdVB) equation with the initial conditions. These solutions include bright and dark solitary wave solutions, triangular solutions and complex line soliton wave solution. These solutions are stable and have applic...