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...

We study the dynamics of BPS string-like objects obtained by lifting monopole and dyon solutions of N = 2 Super-Yang-Mills theory to five dimensions. We present exact traveling wave solutions which preserve half of the supersymmetries. Upon compactification this leads to macroscopic BPS rings in four dimensions in field theory. Due to the fact that the strings effectively move in six dimensions...

In this paper, we study the traveling wave solutions of fractional generalized reaction Duffing equation, which contains several nonlinear conformable time equations. By dynamic system method, phase portraits equation are given, and all possible exact obtained.

In this paper, exact traveling wave solution of Degasperis–Procesi equation can be investigated via the first-integral method. By using the first-integral method which is based on the ring theory of commutative algebra, We construct exact traveling wave solution for Degasperis–Procesi equation , and the obtained solution agrees well with the previously known result.

In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathemati...

This paper is concerned with the extension of the concepts and theories of traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It first introduces the concept of generalized traveling wave solutions of time recurrent and space periodic monostable equations, which extends the concept of periodic traveling wave solutions of time and ...

We study a singularly perturbed system of partial differential equations that models a one-dimensional array of coupled Chua’s circuits. The PDE system is a natural generalization to the FitzHugh-Nagumo equation. In part I of the paper, we show that similar to the FitzHugh-Nagumo equation, the system has periodic traveling wave solutions formed alternatively by fast and slow flows. First, asymp...

Based on Codeço's cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c (∗) is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder's fixed point theorem is applied. The nonexistence of traveling wave solu...

Exact coherent structures are three-dimensional, nonlinear traveling wave solutions of the Navier-Stokes equations. These solutions are typically unstable from onset, yet they capture the basic statistical and structural features of low Reynolds number turbulent shear flows remarkably well. These exact coherent structures have now been found in all canonical shear flows: plane Couette, Poiseuil...

We study the stability of traveling wave solutions to a fifth-order water wave model. By solving a constrained minimization problem we show that “ground state” traveling wave solutions exist. Their stability is shown to be determined by the convexity or concavity of a function d(c) of the wave speed c. The analysis makes frequent use of the variational properties of the traveling waves.