scholarly journals Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: A prototype of strong coupling case

2021 ◽  
Vol 287 ◽  
pp. 236-294
Author(s):  
Yue Ma
2012 ◽  
Vol 26 (27) ◽  
pp. 1250178 ◽  
Author(s):  
JUN YAN

The phase structures of one-dimensional quantum sine-Gordon–Thirring model with N-impurities coupling are studied in this paper. The effective actions at finite temperature are derived by means of the perturbation and non-perturbation functional integrals method. The stability of coexistence phase is analyzed respectively in the weak and strong coupling case. It is shown that the coexistence phase is not stable when fermions have an attractive potential g < 0, and the stable coexistence phase can form when fermions have an exclude potential g > 0.


1991 ◽  
Vol 05 (18) ◽  
pp. 2825-2882 ◽  
Author(s):  
ANGEL SÁNCHEZ ◽  
LUIS VÁZQUEZ

We briefly review the state-of-the-art of research on nonlinear wave propagation in disordered media. The paper is intended to provide the non-specialist reader with a flavor of this active field of physics. Firstly, a general introduction to the subject is made. We describe the basic models and the ways to study disorder in connection with them. Secondly, analytical and numerical techniques suitable for this purpose are outlined. We summarize their features and comment on their respective advantages, drawbacks and applicability conditions. Thirdly, the Nonlinear Klein-Gordon and Schrödinger equations are chosen as specific examples. We collect a number of results that are representative of the phenomena arising from the competition between nonlinearity and disorder. The review is concluded with some remarks on open questions, main current trends and possible further developments.


2017 ◽  
Vol 14 (04) ◽  
pp. 627-670 ◽  
Author(s):  
Yue Ma

Based on the first part, we give a complete proof of the global existence of small regular solutions to a type of quasilinear wave-Klein–Gordon system with null couplings in [Formula: see text] space-time dimension.


2010 ◽  
Vol 140 (5) ◽  
pp. 1011-1039 ◽  
Author(s):  
Hiroaki Kikuchi

AbstractWe study the orbital stability of standing waves for the Klein–Gordon–Schrödinger system in two spatial dimensions. It is proved that the standing wave is stable if the frequency is sufficiently small. To prove this, we obtain the uniqueness of ground state and investigate the spectrum of the appropriate linearized operator by using the perturbation method developed by Genoud and Stuart and Lin and Wei. Then we apply to our system the general theory of Grillakis, Shatah and Strauss.


2003 ◽  
Vol 06 (04) ◽  
pp. 507-514 ◽  
Author(s):  
DAFANG ZHENG ◽  
GÜLER ERGÜN

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in both networks. The model segregates the links in the networks as intra-links, cross-links and mix-links. The corresponding degree distributions of these links are found to be power-laws with exponents having coupled parameters for intra- and cross-links. In the weak coupling case, the model reduces to a simple citation network. As for the strong coupling, it mimics the mechanism of the web of human sexual contacts.


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