We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the...

The nonlinear Klein–Gordon equation with a different potential that satisfies the degeneracy properties discussed in this paper possesses solitonic solutions that interact with long-range forces. We generalize the Ginzburg–Landau equation in such a way that the topological defects supported...