An analytic study of two nonlinear variants of the (2+1)-dimensional Camassa-Holm-KP equation is presented in this paper. The (G'/G)-expansion method is employed to obtain exact travelling wave solutions of the equations. The solutions gained from the proposed method have been verified with those obtained by the sine-cosine method and the tanh method. More importantly, other new and more genera...

The modified method of simplest equation is applied to the extended Korteweg de Vries equation and to generalized Camassa Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained. The equations of Bernoulli, Riccati and the extended tanh equation are used as simplest equations. Some of the obtained solutions correspond to surface water wav...

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...

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...

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 research area of nonlinear partial differential equations (NLPDEs) has been very active for the past few decades. The study of the exact solutions of a nonlinear evolution equation (NLEE) plays an important role to understand the nonlinear physical phenomena which are described by these equations. In recent years several powerful and efficient methods have been developed for finding analyti...

1. Introduction In the past few years, computation of definite integrals to high precision has emerged as a very useful tool in experimental mathematics. In particular, it is often possible to recognize an otherwise unknown definite integral in analytic terms, provided its numerical value can be calculated to high accuracy. As a single example, recently the author, together with Jonathan Borwei...

initiated by Dodd and Bullough [1] and Žiber and Šabat [2], plays a significant role in many scientific applications such as solid state physics, nonlinear optics, and quantum field theory. There are many research works for Dodd-Bullough equation in the last decades. It is shown thatDodd-Bulloughdetermines the intrinsic geometry of the two-dimensional affine sphere in the three-dimensional unim...