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Asymptotic behavior of solutions of defocusing integrable discrete nonlinear schrodinger equation

Frontiers of Mathematics in China 2013年第5期8卷 1077-1083页

作者： Hideshi YAMANE Department of Mathematical Sciences Kwansei Gakuin University Sanda 669-1337 Japan

We report our recent result about the long-time asymptotics for the defocusing integrable discrete nonlinear schrodinger equation of Ablowitz- Ladik. The leading term is a sum of two terms that oscillate with decay of... 详细信息

关键词： discrete nonlinear schrodinger equation Ablowitz-Ladik model,asymptotics inverse scattering transform nonlinear steepest descent

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Self-Trapping in discrete nonlinear schrodinger equation with Next-Nearest Neighbor Interaction

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Communications in Theoretical Physics 2013年第5期59卷 643-648页

作者：王燕 Department of Mathematics Shanghai University Department of Mathematics Luoyang Normal University

The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with nextnearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using localized initial conditions, the time-averaged occupation probability of the initial site is investigated which is a function of the degree of nonlinearity and the linear coupling strengths. The self-trapping transition occurs at larger values of the nonlinearity parameter as the NNN coupling strength of the lattice increases for fixed size. Furthermore, given NNN coupling strength, the self-trapping properties for different sizes are considered which are some different from the case with general nearest neighbor (NN) interaction.

关键词： discrete nonlinear schrodinger equation next-nearest neighbor interaction symplectic integrator nonlinear lattices

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Non-Nehari Manifold Method for Periodic discrete Superlinear Schr(o|¨)dinger equation

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Acta Mathematica Sinica,English Series 2016年第4期32卷 463-473页

作者： Xian Hua TANG School of Mathematics and Statistics Central South University

We consider the nonlinear difference equations of the form Lu=f（n,u）,n∈Z,where L is a Jacobi operator given by（Lu）（n）=a（n）u（n＋1）＋a（n-1）u（n-1）＋b（n）u（n） for n ∈Z,{a（n）} and {b（n）} are real valued N-periodic sequences,and f（n,t） is superlinear on t.Inspired by previous work of Pankov[discrete Contin.Dyn.Syst.,19,419-430（2007）]and Szulkin and Weth[J.Funct.Anal.,257,3802-3822（2009）],we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f.Unlike the Nehari manifold method,the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.

关键词： discrete nonlinear schrodinger equation non-Nehari manifold method superlinear ground state solutions of Nehari-Pankov type

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Standing Waves for discrete nonlinear schrodinger equations with Nonperiodic Bounded Potentials

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Acta Mathematicae Applicatae Sinica 2019年第2期35卷 374-385页

作者： Tie-shan HE Meng ZHANG Kai-hao LIANG Peng-fei GUO College of Computation Science Zhongkai University of Agriculture and Engineering

In this paper, we investigate standing waves in discrete nonlinear Schr?dinger equations with nonperiodic bounded potentials. By using the critical point theory and the spectral theory of self-adjoint operators, we prove the existence and infinitely many sign-changing solutions of the equation. The results on the exponential decay of standing waves are also provided.

关键词： discrete nonlinear schrodinger equation Standing wave Nonperiodic bounded potential Sign-changing solution Critical point theory

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