Nonlinear evolution equations have a major role in various scientific and engineering fields, such as fluid mechanics, plasma physics, optical fibers, solid state physics, chemical kinematics, chemical physics and geochemistry. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. In recent years, quite a few meth...

In this paper, we revise two commonly used saturated functions, the logistic sigmoid and the hyperbolic tangent (tanh). We point out that, besides the well-known non-zero centered property, slope of the activation function near the origin is another possible reason making training deep networks with the logistic function difficult to train. We demonstrate that, with proper rescaling, the logist...

In this work, various dispersion compensation methods are designed and evaluated to search for a cost-effective technique with remarkable dispersion compensation and a good pulse shape. The techniques consist of different chirp functions applied to a tanh fiber Bragg grating (FBG), a dispersion compensation fiber (DCF), and a DCF merged with an optimized linearly chirped tanh FBG (joint techniq...

1. Introduction In the past few years, computation of definite integrals to high precision has emerged as a very useful tool in experimental mathematics. In particular, it is often possible to recognize an otherwise unknown definite integral in analytic terms, provided its numerical value can be calculated to high accuracy. As a single example, recently the author, together with Jonathan Borwei...

A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Parallels are drawn through discussion and example to the tan...

We consider the generalized integrable fifth order nonlinear Korteweg-de Vries (fKdV) equation. The extended Tanh method has been used rigorously, by computational program MAPLE, for solving this fifth order nonlinear partial differential equation. The general solutions of the fKdV equation are formed considering an ansatz of the solution in terms of tanh. Then, in particular, some exact soluti...

Convolutional Neural Network (CNN) is a deep learning model which has been an active research topic and applied extensively to vibration data for condition monitoring (CM). In CNN, hyper-parameters, such as activation function, have significant effect on the training task and, consequently, overall performance of network. The existing functions some limitations, vanishing gradient problem, dead...

The hyperbolic tangent (tanh) method is a powerful technique to symbolically compute traveling waves solutions of one-dimensional nonlinear wave and evolution equations. In particular, the method is well suited for problems where dispersion, convection, and reactiondiffusion phenomena play an important role. The technique is outlined for the computation of closedform tanh-solutions for nonlinea...

Foaming occurs in many distillation and absorption processes. The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. In this paper, we use a semi analytic method, the Adomian decomposition method, and an analytic method, the tanh method to handle the foam drainage equation. The powerful tanh method gives the solution in a closed form. However, Adomi...