We show that wave maps φ from two-dimensional Minkowski spaceR to hyperbolic spacesH are globally smooth in time if the initial data is smooth, conditionally on some reasonable claims concerning the local theory of such wave maps, as well as the self-similar and travelling (or stationary solutions); we will address these claims in the sequels [67], [68], [69], [70] to this paper. Following rece...

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher–Kolmogorov–Petrovskii–Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Klein-Gordon chains are one-dimensional lattices of nonlinear oscillators in an anharmonic on-site potential, linearly coupled with their first neighbours. In this paper, we study the existence in such networks of spatially localized solutions, which appear time periodic in a referential in translation at constant velocity. These solutions are called travelling breathers. In the case of travell...

In this paper, by using the improved ( ′ G )-expansion method, we have successfully obtained some travelling wave solutions of the variant Boussinesq Equations. These exact solutions include the hyperbolic function solutions, trigonometric function solutions and rational function solutions. Mathematics Subject Classification: 35Q58; 37K50

In a recent paper [Abazari R. Application of ( ′ G )-expansion method to travelling wave solutions of three nonlinear evolution equation. Computers & Fluids 2010;39:1957–1963], the (G/G)-expansion method was used to find travelling-wave solutions to three nonlinear evolution equations that arise in the mathematical modelling of fluids. The author claimed that the method delivers more general fo...

We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term γ and a linear dissipative term, and the equation is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We determine all travelli...