Traveling Wave Solutions in an Integrodifference Equation with Weak Compactness

This article studies the existence of traveling wave solutions inan integrodifference equation with weak compactness. Because of the specialkernel function that may depend on the Dirac function, traveling wave mapshave lower regularity such that it is difficult to directly look for a traveling wavesolution in the uniformly continuous and bounded functional space. In thispaper, by introducing a proper set of potential wave profiles, we can obtainthe existence and precise asymptotic behavior of nontrivial traveling wavesolutions, during which we do not require the monotonicity of this model.