In this paper we make a full analysis of the symmetry reductions beam equation by using classical Lie method infinitesimals and nonclassical method. We consider travelling wave depending on form an arbitrary function. have found several new classes solutions that not been considered before: expressed in terms Jacobi elliptic functions, Wadati solitons compactons. Several coherent structures are...

In this paper, we derive exact traveling wave solutions of the (2+1)-dimensional Nizhnik-NovikovVeselov (NNV) system by a presented method. The method appears to be efficient in seeking exact solutions of nonlinear equations. Key–Words: (G ′ G )-expansion method, Travelling wave solutions, (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) system, nonlinear equation, exact solution, evolution equa...

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompo...

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions...

In this paper, we employ the bifurcation method of dynamical systems to investigate the exact travelling wave solutions for the Fornberg-Whitham equation ut − uxxt + ux+uux = uuxxx+3uxuxx. The implicit expression for solitons is given. The explicit expressions for peakons and periodic cusp wave solutions are also obtained. Further, we show that the limits of soliton solutions and periodic cusp ...

In this paper we research the exact solutions for a sort of new Sine-Gordon equation. By using the tanh method and a variable separated ordinary difference method, we get some new exact travelling wave solutions, among which there are two new noncontinuous wave solutions.

Many oscillatory biological systems show periodic travelling waves. These are often modelled using coupled reaction–diffusion equations. However, the effects of different movement rates (diffusion coefficients) of the interacting components on the predictions of these equations are largely unknown. Here we investigate the ways in which varying the diffusion coefficients in such equations alters...

Under the travelling wave transformation, Calogero-Degasperis-Focas equation was reduced to an ordinary differential equation. Using a symmetry group of one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE. Furthermore, we applied the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classific...