In this paper, we investigate the new traveling wave solutions for sixth-order Boussinesq equation using tanh-coth method. Such a method is type of expansion that represents partial differential equations as polynomials $\tanh$ and $\coth$ functions. We discover several with different parameters, which are fundamental importance various applications.

In writing this last expression, we have used the fact that the integrand is now convergent at large x. The upper limit of the integral βch̄ωc/2 >> 1 in all known cases of superconductivity, so we take the upper limit to infinity. In evaluating the first term note that the limit x → 0 of ln(x)Tanh(x) is convergent even though ln(x) diverges as x→ 0. The integral that remains is a tabulated defin...

Abstract. Inversion formulas have been found, converting between Stirling, tanh and Lah numbers. Tanh and Lah polynomials, analogous to the Stirling polynomials, have been defined and their basic properties established. New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations. In the second part of the paper, it has been shown that if ...

We introduce in this paper a new chaotic map with dynamical properties controlled by two free parameters. The map definition is based on the hyperbolic tangent function, so it is called the tanh map. We demonstrate that the Lyapunov exponent of the tanh map is robust, remaining practically unaltered with the variation of its parameters. As the main application, we consider a chaotic communicati...

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...

This paper presents fast and accurate algorithms for computing the prices of discretely sampled lookback options. Under the Black-Scholes framework, the pricing of a discrete lookback option can be reduced to a series of convolutions of a function with the Gaussian distribution. Using this fact, an efficient algorithm, which computes these convolutions by a combination of the double-exponential...

and Applied Analysis 3 Table 1: The operations for generalized differential transform method. Original function Transformed function f n, t g n, t h n, t F n, k G n, k H n, k f n, t αg n, t F n, k αG n, k f n, t ∂g n, t /∂t F n, k k 1 G n, k 1 f n, t g n, t h n, t F n, k ∑k r 0 G n, r H n, k − r f n, t ∂g n, t /∂t F n, k k m G n, k m f n, t g n s, t F n, k G n s, k To improve the accuracy and c...