Perturbed Schrödinger lattice systems with superlinear terms: Multiplicity of homoclinic solutions

2021 ◽  
Vol 60 (5) ◽  
Author(s):  
Guanwei Chen ◽  
Shiwang Ma
Keyword(s):  
Homoclinic Solutions ◽  
Lattice Systems

Perturbed Schrödinger lattice systems: existence of homoclinic solutions

2018 ◽  
Vol 149 (04) ◽  
pp. 1083-1096 ◽  
Author(s):  
Guanwei Chen ◽  
Shiwang Ma
Keyword(s):  
Ground State ◽  
Homoclinic Solutions ◽  
Lattice Systems ◽  
Published Result

AbstractWe study a class of Schrödinger lattice systems with sublinear nonlinearities and perturbed terms. We get an interesting result that the systems do not have nontrivial homoclinic solutions if the perturbed terms are removed, but the systems have ground state homoclinic solutions if the perturbed terms are added. Besides, we also study the continuity of the homoclinic solutions in the perturbation terms at zero. To the best of our knowledge, there is no published result focusing on the perturbed Schrödinger lattice systems.

Elastic scattering from cubic lattice systems with paracrystalline distortion. II

1990 ◽  
Vol 41 (6) ◽  
pp. 3854-3856 ◽  
Author(s):  
Hideki Matsuoka ◽  
Hideaki Tanaka ◽  
Norio Iizuka ◽  
Takeji Hashimoto ◽  
Norio Ise
Keyword(s):  
Elastic Scattering ◽  
Lattice Systems ◽  
Cubic Lattice

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

Transition from particlelike to wavelike behavior for an electron in one-dimensional nonuniform lattice systems

2016 ◽  
Vol 94 (3) ◽  
Author(s):  
Longyan Gong ◽  
Bingjie Xue ◽  
Wenjia Li ◽  
Weiwen Cheng ◽  
Shengmei Zhao
Keyword(s):  
Lattice Systems ◽  
One Dimensional
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