Analytic Solitary-wave Solutions for Modified

Re- cently, based on the Hirota bilinear method, Nakamura in his two serial papers [10, 11] proposed a conve- nient way to construct a kind of quasi-periodic so- lutions of

The bilinear method can trans- form some NLPDEs into bilinear equations, e.g., the Korteweg–de Vries (KdV) [10], Gardner [27 – 32], Kadomtsev–Petviashvili (KP) [33 – 36] and

Recently, many powerful methods have been estab- lished and developed to carry out the integrations of NLPDEs of all kinds, such as the subsidiary ordinary differential equation

With three auxiliary convergence-control parameters, whose possible optimal values can be obtained by minimizing the averaged residual error, the method used here provides us with

With three auxiliary convergence-control parameters, whose possible optimal values can be obtained by minimizing the averaged residual error, the method used here provides us with

In this work we study two partial differential equations that constitute second- and third-order approximations of water wave equations of the Korteweg – de Vries type. In

In this paper we have used a simple assump- tion and have found new solitary wave solutions for equations (1.4) and (1.5), that represent, respectively, second- and

Distributions of the (a) number of waves per train, (b) amplitude of stable (light bars) and unstable (dark bars) waves, (c) propagation depth of all waves and of ingoing (light