[PDF] Top 20 The Tanh Methods for the Hirota Equations

... Physically, the NLS equation describes the modulation of weakly-nonlinear wave trains. In deep water. Benjamin and Feir [Benjamin and Feir(1967)] showed that an uniform wave train is unstable to long wave perturbations. ... See full document

... differential equations (PDEs) appears in describing the nonlinear phenomena in various fields of ...powerful methods have been developed to find the exact solutions of non- linear PDEs, among them inverse ... See full document

... the tanh and Sech function methods are proposed to establish a traveling wave solution for nonlinear partial differential ...two methods are used to obtain new solitary wave solutions for ... See full document

... the methods for deriving exact solutions for the governing equations have to be ...powerful methods have been established and improved. Among these methods, we cite the tanh and ... See full document

... differential equations and partial differential equations are quite ...many methods have been proposed by many authors for finding exact solutions of nonlinear differential ...here: tanh − ... See full document

... Different methods have their different types of specific applications for nonlinear evolution ...new methods for solving PDEs which based on the original method, such as Hirota’s bilinear method [1], ... See full document

... differential equations which has long been a major concern for both mathematicians and ...differential equations, when they exist, is very important to the understanding of most non-linear physical ... See full document

... Burgers’ equations have played an important role in many physical applications such as investigating the shallow water waves and modeling of gas dynamics [5] ...burgers’ equations many researchers have been ... See full document

... of methods have been proposed in the litera- ture recently for solving different kinds of physical and mathematical ...those methods are: the homotopy perturbation method [1-7], the variational it- eration ... See full document

... powerful methods have been proposed to obtain exact solutions of nonlinear evolution equations, such as tanh-sech function method [1, 2, 3, 4], extended tanh function method [5, 6, 7, 8], ... See full document

... standard Hirota equation, so that we refer to them as nonlocal Hirota equations ...The equations possess two types of solutions of qualitatively different behaviour and parameter ...solution ... See full document

... additional methods to adapt these spectral shifts to increase ...adaptive-spectral-shift methods together with the stability improvements in de- flatory ...− tanh s was used as the denoising ... See full document

... The review presents the main methods for the preparation of modified polyorganosiloxanes (POS) containing amino groups. Modified POS are the most important functional compounds for the synthesis of polyimide and ... See full document

... In this paper architecture for separation of more than two linearly mixed speech signals by ICA is improved by using discrete wavelet transform along with ICA. It contains two parallel processes, one process takes the ... See full document

... two methods for transferring of Communication among the ...two methods known as Clique and Cluster as shown in [8].In these methods a Node call the Monitor Node commences the discovering ... See full document

... [5] J. Hietarinta, “A Search for Bilinear Equations Passing Hirota’s Three-Soliton Condition. I. KdV-Type Bilinear Equations,” Journal of Mathematical Physics, Vol. 28, No. 8, 1987, pp. 1732-1742. ... See full document

... The rest of this article is arranged as follows. In Section , the basic ideas of the first integral method are expressed. In Section , the method is employed for obtaining the exact solutions of double sine-Gordon (SG) ... See full document

... In this subsection, we consider the case of parameter c =  in the seed solution of the gen- eral Hirota equation (), which we will start with the plane wave seed solution. Without loss of generality, assuming ... See full document

... Maxwell’s equations were confirmed to be consistent. Using the generated equations of motion of charged particles including the representation of E and B in terms of scalar and vector potentials, other ... See full document

... Optimization criteria can be divided into two types: criteria that are connected with the time of the completion of a job, and criteria connected with costs. W hen planning dates and capacities, we usually use different ... See full document