The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To ver...

In this paper, a generalized F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the (2 + 1)dimensional breaking soliton equations to illustrate the validity and advantages of the proposed method. As a result, many new and more general non-travelling wave and coefficient function solutions are obtained includin...

In this paper, using modified FF-expansion method, we present some explicit formulas of exact traveling wave solutions for the foam drainage equation. A modified FF-expansion method is proposed by taking full advantages of FF-expansion method and Riccati equation in seeking exact solutions of non-linear partial differential equations.

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-ellipti...

After antigenic stimulation, CD8(+) T cells undergo clonal expansion and differentiation into CTLs that can mount a strong defense against intracellular pathogens and tumors. SWAP-70-like adapter of T cells (SLAT), also known as Def6, is a novel guanine nucleotide exchange factor for the Cdc42 GTPase and plays a role in CD4(+) T cell activation and Th cell differentiation by controlling Ca(2+)/...

We propose an empirical method for estimating term weights directly from relevance judgements, avoiding various standard but potentially troublesome assumptions. It is common to assume, for example, that weights vary with term frequency (t f ) and inverse document frequency (idf) in a particular way, e.g., t f . idf, but the fact tha t there are so many variants of this formula in the literatur...

In this study, a stochastic model for transient saturated–unsaturated flow is developed based on the Karhunen-Loeve expansion of the input random soil properties combined with a perturbation method. The log-transformed saturated hydraulic conductivity f ðxÞ and the soil pore size distribution parameter aðxÞ are assumed to be normal random functions with known covariances. We decompose f ðxÞ and...

The periodic wave solution for the generalized Hirota-Satsuma system was obtained by using the F-expansion method which can be thought of as a generalization of the Jacobi elliptic function method proposed recently. The Adomian decomposition method is used to solve the same system numerically and the approximate solution is compared with the exact solution. Moreover, we analyze the absolute err...