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This paper is based on finding the exact solutions for Burger's equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs. [ABSTRACT FROM AUTHOR]

Abstract: In general, shape of an on-line signature is used as a single discriminating feature. Sometimes shape of signature is used alone for verification purposes and sometimes it is used in combination with some other dynamic features such as velocity, pressure and acceleration. The shape of an on-line signature is basically formed due to the wrist and fingers movements where the wrist movement is represented by the horizontal trajectory and the movement of the fingers is represented by vertical trajectory. As the on-line signature is formed due to the combination of two movements that are essentially independent of each other, it will be more effective to use them as two separate discriminating features. Based on this observation, we propose to use these trajectories in isolation by first decomposing the pressure and velocity profiles into two partitions and then extracting the underlying horizontal and vertical trajectories. So the overall process can be thought as the process which exploits the inter-feature dependencies by decomposing signature trajectories depending upon pressure and velocity information and performs verification on each partition separately. As a result, we are able to extract eight discriminating features and among them the most stable discriminating feature is used in verification process. Further Principal Component Analysis (PCA) has been proposed to make the signatures rotation invariant. Experimental results demonstrate superiority of our approach in on-line signature verification in comparison with other techniques. [Copyright &y& Elsevier]

In this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs. [ABSTRACT FROM AUTHOR]