We consider traveling wave solutions to a class of diierential-diierence equations. Our interest is in understanding propagation failure, directional dependence due to the discrete Laplacian, and the relationship between traveling wave solutions of the spatially continuous and spatially discrete limits of this equation. The diierential-diierence equations that we study include damped and undamp...

We study entire solutions of a two-component competition system with LotkaVolterra type nonlinearity in a lattice. It is known that this system has traveling wave front solutions and enjoys comparison principle. Based on these solutions, we construct some new entire solutions which behave as two traveling wave fronts moving towards each other from both sides of x-axis.

Email: [email protected] Abstract: The enhanced (G′/G)-expansion method is very effective and powerful method to find the exact traveling wave solutions of nonlinear evolution equations. We choose the Phi-4 equation to illustrate the validity and advantages of this method. As a result, many exact traveling wave solutions are obtained, which include soliton, hyperbolic function and trigonom...

Under the traveling wave transformation, Fornberg-Whitham equation is reduced to an ordinary differential equation whose general solution can be obtained using the factorization technique. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtain the classification of all single traveling wave solutions to ...

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.

We investigate the qualitative behavior of solutions of a Burgers-Boussinesq system – a reaction-diffusion equation coupled via gravity to a Burgers equation – by a combination of numerical, asymptotic and mathematical techniques. Numerical simulations suggest that when the gravity ρ is small the solutions decompose into a traveling wave and an accelerated shock wave moving in opposite directio...

This paper is concerned with the asymptotic behavior of the trav-eling wave fronts in Lotka-Volterra competition system. By Laplacian transform, we prove that the traveling wave fronts of the system grow exponentially when the traveling coordinate tends to negative infinity.

In this paper, the (G′/G)-expansion method is applied to seek traveling wave solutions of the combined and the double combined sinh-cosh-Gordon equations. This traveling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. It is shown that the proposed method is direct, effective and more general. 2000 Mathematics Subject Classification: 35K01; 35J05.

By using Schauder’s Fixed Point Theorem, we study the existence of traveling wave fronts for reaction-diffusion systems with spatio-temporal delays. In our results, we reduce the existence of traveling wave fronts to the existence of an admissible pair of upper solution and lower solution which are much easier to construct in practice.

Thermoacoustic (TA) heat engines are engines which convert heat into acoustic power. This relatively new class of heat engines gains commercial interest, because of their low number of moving parts and high potential efficiency [1]. Especially traveling wave thermoacoustic engines are capable of reaching this high efficiency, because traveling wave engines perform a thermodynamic cycle similar ...