Bright compact breathers.
In this communication we will consider the potential of some general classes of nonlinear lattice models to support bright discrete compact breather solutions (compactlets). We analyze the conditions for which such solutions are possible and classify the models as belonging in three general categories: a class with no compact breather solutions, one with one-parameter families of solutions, and a class with "isolated" solutions (i.e., no free parameters). In the latter two cases we construct the solutions and analyze their linear stability. The drastically different stability features of these solutions in comparison with their smoothly decaying counterparts are discussed. Stable breather solutions with compact support are identified in the one-parameter families of solutions, while the corresponding solutions found in the zero-parameter families are always found to be unstable.
Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003-4515, USA. kevrekid@math.umass.edu
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