Gap solitons in periodic discrete nonlinear Schrödinger equations
By Alexander Pankov. 2005
158 citations recorded by the source corpus.
It is shown that the periodic discrete nonlinear Schrödinger equation, with cubic nonlinearity, possesses gap solutions, i.e. standing waves, with the frequency in a spectral gap, that are exponentially localized in the spatial variable. The proof is based on the linking theorem in combination with periodic approximations.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/68fcaaeb1b0e057a875d70fd675f55d16364072a
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In Mathematical Physics
- Antonio Iannizzotto
- Stepan A. Tersian
- Jianshe Yu
- Zhan Fang Zhou
- Guoping Zhang
- Alexander Pankov
- Yuming Chen
- Pasquale Candito
In Statistical and Nonlinear Physics
Citations in the corpus
- On the existence of homoclinic solutions of a class of discrete nonlinear periodic systems (2010, background): “1) was considered in [19,20] when fn(u) = χnu(3).”
- Homoclinic solutions in periodic difference equations with saturable nonlinearity (2011, background): “Recently, Pankov [20, 21 ] considered the gap solitons of the following periodic DNLS equation”
- Multiple homoclinic solutions for the discrete p-Laplacian via critical point theory (2013, methodology): “Another type of arguments based on variational methods and periodicity are applied by Pankov [23] to the discrete Schrödinger equation.”
- STANDING WAVES OF THE DISCRETE NONLINEAR SCHR ¨ ODINGER EQUATIONS WITH GROWING POTENTIALS (2008, background): “In this paper we use Nehari manifold approach and compact embedding theorem to prove the existence of nontrivial solutions of (3.1) for the case σ = 1; ω 13 ]) to prove the similar results that will be addressed in our another upcoming paper.”