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Zbl 1200.37072
Zhang, Guoping
Breather solutions of the discrete nonlinear Schrödinger equations with unbounded potentials. (English)
[J] J. Math. Phys. 50, No. 1, Paper No. 013505, 12 p. (2009). ISSN 0022-2488; ISSN 1089-7658/e

Summary: In this paper the author investigates the existence of nontrivial breather solutions of the discrete nonlinear Schrödinger equation with the unbounded potential at infinity. First he derives a discrete version of compact embedding theorem. Then combining the Nehari manifold approach and the compact embedding theorem, he shows the existence of breather solutions without Palais-Smale condition. The results on the exponential decay of breather solutions are also provided in this paper. Editorial remark: No review copy delivered.

MSC 2000:: *37K60 Lattice dynamics
37K40 Soliton theory, asymptotic behavior of solutions

Keywords: eigenvalues and eigenfunctions; nonlinear equations; Schrödinger equation; waves

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Zentralblatt MATH Berlin [Germany]