Breather solutions in conservative and dissipative nonlinear Klein–Gordon lattices

IF 1.4 3区数学 Q1 MATHEMATICS

Journal of Fixed Point Theory and Applications Pub Date : 2024-04-29 DOI:10.1007/s11784-024-01106-x

Dirk Hennig

引用次数: 0

Abstract

We study time-periodic and spatially localised solutions (breathers) in general infinite conservative and dissipative nonlinear Klein–Gordon lattices. First, in the time-reversible (conservative) case, we give a concise proof of the existence of breathers not using the concept of the anticontinuous limit. The existence problem is converted into an operator equation for time-reversal initial conditions generating breather solutions. A nontrivial solution of this operator equation is established facilitating Schauder’s fixed point theorem. Afterwards, we prove the existence and uniqueness of breather solutions in damped and forced infinite nonlinear Klein–Gordon lattice systems utilising the contraction mapping principle.

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保守和耗散非线性克莱因-戈登网格中的呼吸解

我们研究一般无限保守和耗散非线性克莱因-戈登网格中的时间周期和空间局部解（呼吸器）。首先，在时间可逆（保守）情况下，我们给出了不使用反连续极限概念的呼吸器存在性的简明证明。存在性问题被转化为一个产生呼吸解的时间逆转初始条件的算子方程。这个算子方程的非微观解的建立促进了 Schauder 定点定理。随后，我们利用收缩映射原理证明了阻尼和强迫无限非线性克莱因-戈登晶格系统中呼吸解的存在性和唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Fixed Point Theory and Applications 数学-数学

CiteScore

3.10

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Fixed Point Theory and Applications (JFPTA) provides a publication forum for an important research in all disciplines in which the use of tools of fixed point theory plays an essential role. Research topics include but are not limited to: (i) New developments in fixed point theory as well as in related topological methods, in particular: Degree and fixed point index for various types of maps, Algebraic topology methods in the context of the Leray-Schauder theory, Lefschetz and Nielsen theories, Borsuk-Ulam type results, Vietoris fractions and fixed points for set-valued maps. (ii) Ramifications to global analysis, dynamical systems and symplectic topology, in particular: Degree and Conley Index in the study of non-linear phenomena, Lusternik-Schnirelmann and Morse theoretic methods, Floer Homology and Hamiltonian Systems, Elliptic complexes and the Atiyah-Bott fixed point theorem, Symplectic fixed point theorems and results related to the Arnold Conjecture. (iii) Significant applications in nonlinear analysis, mathematical economics and computation theory, in particular: Bifurcation theory and non-linear PDE-s, Convex analysis and variational inequalities, KKM-maps, theory of games and economics, Fixed point algorithms for computing fixed points. (iv) Contributions to important problems in geometry, fluid dynamics and mathematical physics, in particular: Global Riemannian geometry, Nonlinear problems in fluid mechanics.