In this paper we use the modified tanh-coth method to solve the Kawahara and the modified Kawahara equations. New multiple traveling wave solutions are obtained for the Kawahara and the modified Kawahara equations. 2000 Mathematics Subject Classification: 35K01; 35J05.

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second ...

We consider the problem of the evolution of the fine structure coefficient α under the assumption that the scalar field coupling to the Maxwell term satisfies the condition mt ≫ 1 for coherent dark matter oscillations. In this case we find that the coupling scale f in the leading order coupling −(φ/4f)FμνF μν affects the cosmological evolution of α according to ln(α/α0) ∝ ξ(mPl/f)× ln(tanh(t/2τ...

The capability of Extended tanh–coth, sine–cosine and Exp-Function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed. In this study, the generalized nonlinear Schrödinger (GNLS) equation is solved by three different methods. To obtain the single-soliton solutions for the equation, t...

Neural network is a popular method used in machine research, and activation functions, especially ReLu Tanh, have very important function neural networks, to minimize the error value between output layer target class. With variations number of hidden layers, as well neurons each different layer, this study analyzes 8 models classify Titanic's Survivor dataset. The result that has better perform...

BACKGROUND The Bayesian approach is one alternative for estimating correlation coefficients in which knowledge from previous studies is incorporated to improve estimation. The purpose of this paper is to illustrate the utility of the Bayesian approach for estimating correlations using prior knowledge. METHODS The use of the hyperbolic tangent transformation (rho = tanh xi and r = tanh z) enab...

The problem of determining if a bivariate normal correlation changes with respect to time or some other covariate is considered. It is assumed that the means and standard deviations of the normal random variables can be consistently estimated from the entire data run, and do not need to be re-estimated for each covariate value. A new estimator of a bivariate normal correlation is given that has...

The nonlinear equations of mathematical physics are major subjects in physical science [1]. Recently many new approaches for finding the exact solutions to nonlinear wave equations have been proposed, for example, tanh-sech method [2–4], extended tanh method [5–7], sine-cosine method [8–10], homogeneous balance method [11, 12], Jacobi elliptic function method [13–16], F -expansion method [17–19...