In this paper, using the tanh-function method, we introduce a new approach to solitary wave solutions for solving nonlinear PDEs. The proposed method is based on adding integration constants to the resulting nonlinear ODEs from the nonlinear PDEs using the wave transformation. Also, we use a transformation related to those integration constants. Some examples are considered to find their exact ...

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solution...

The modified tanh method is one of most direct and effective algebraic method for obtaining exact solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones. In this paper,we look for exact soliton solutions of the improved Eckhaus equation and the (2+1)-dimensional improved Eckhaus equation. 2000 Mathematics Subject...

We propose a novel activation function that implements piecewise orthogonal non-linear mappings based on permutations. It is straightforward to implement, and very computationally efficient, also it has little memory requirements. We tested it on two toy problems for feedforward and recurrent networks, it shows similar performance to tanh and ReLU. OPLU activation function ensures norm preserva...

In this paper, tanh method is applied to obtain exact solutions for two systems of nonlinear wave equations, namely, two component evolutionary system of homogeneous KdV equations of order 3 (type I as well as type II). Moreover, traveling wave hypothesis is used to obtain sech solution of type II coupled KdV system, in a more general setting. The results show that this method presents exact so...

Let us assume we are given a random variable m. It was Beltrami who first asked whether leftConway–Cartan arrows can be constructed. We show that π > Ω (−∞א0, . . . ,Fi). In [8], it is shown that 1 א0 ∼ lim ←− (0,−1)× log (1) ≡ √ 2 ∐ T =π tanh ( 1 i ) ± 0 ∩D = { ĝ : y ( 0 ) > sinh ( א0 ) − kE,σ (א0, ‖Hq‖) } . Here, compactness is obviously a concern.

A direct approach with computerized symbolic computation is applied to construct a series of traveling wave solutions for nonlinear equations. Compared with most existing symbolic computation methods such as tanh method and Jacobi function method, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the solution accord...

Abstract. The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2×2 Hamiltonian with the tanh-type plus sech-type energy difference and with constant off-diagonal elements as an example to show the efficiency of the monodromy ...

The activation function has a critical influence on whether convolutional neural network in deep learning can converge or not; proper not only makes the faster but also reduce complexity of architecture and gets same better performance. Many functions have been proposed; however, various advantages, defects, applicable architectures. A new called Polynomial Linear Unit (PolyLU) is proposed this...