A remark on the existence of breather solutions for the Discrete Nonlinear Schr'odinger Equation in infinite lattices: The case of site dependent anharmonic parameter

摘要

We discuss the existence of breather solutions for a Discrete NonlinearSchr\"odinger equation in an infinite $N$-dimensional lattice, involving sitedependent anharmonic parameter. We give a simple proof on the existence of(nontrivial) breather solutions based on variational approach, assuming thatthe sequence of anharmonic parmeters is in an appropriate sequence space(decays with an appropriate rate). We also give a proof on the non-existence of(non-trivial) breather solutions, and discuss a possible physicalinterpretation of the restrictions, both in the existence and nonexistencecase.