This paper describes properties of the tanh function from the standpoint of its use in robust signal processing and statistical estimation. It has recently been shown that the construction of circuits that perform tanh is very natural in present integrated circuit technology. Therefore, this transform is likely to become widely used in circuits that perform computations on (noisy) input signals...

In this paper, the sine-cosine, the standard tanh and the extended tanh methods has been used to obtain solutions of the KadomstevPetviashvili(KP) equation. New solitons solutions and periodic solutions are formally derived. The change of parameters, that will drastically change characteristics of the equation, is examined.

Information fusion at the matching score level is widely used, due to the simplicity in combining the scores generated by different matchers. Since the matching scores output by various modalities are diverse in numerical range, score normalization is needed first, to transform these scores into a common domain. Then score fusion is to be carried out on the normalized scores. In this paper, we ...

In this paper, the hyperbolic tangent function (tanh) method is used in finding soliton solutions of Generalized Fisher Equation (GFE) and Spalding Equation (SE). It is shown that the tanh method provides a straight forward and powerful tool for solving Nonlinear Evolution Equations (NLEEs) in Mathematical Physics.

In recent years, nonlinear phenomena play a crucial role in appliedmathematics and physics. Directly searching for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive partly due to the availability of computer symbolic systems like Mathematica or Maple that allow us to perform some complicated and tedious algebraic calculation on a computer as ...

1. Mittag-Leffler's polynomial gn(z) has the orthogonal property fgm(-ix)gn(ix)dx/xsh(x) = m $ n m > 0-co =-2/n m=n n>O. (1.1) This is readily obtained by inverting the integral representation' co gn(ix) = (1/ir) sin (irx)f exu (tanh '/2u)ndu/sh u n > 1 (1.2)-co0 by means of Fourier's inversion formula. The resulting equation co cosech u (tanh 1/2u)n = 1/2 e-iux cosech (irx)gn(ix)dx (1.3)-OD th...

The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions an...

Based on an extended tanh-function method, a general method is suggested to obtain multiple travelling wave solutions for nonlinear partial differential equations (PDEs). The validity and reliability of the method is tested by its application to some nonlinear PDEs. The obtained results are compared with that of an extended tanh-function method and hyperbolic-function method. New exact solution...