摘要:

AbstractThis is the First part of a two‐part series on forced lattice vibrations in which a semi‐infinite lattice of one‐dimensional particles {xn}n≧1is driven from one end by a particlex0. This particle undergoes a given, periodically perturbed, uniform motion,x0(t) =at+h(yt), whereaand γ are constants andh(·) has period 2π. For a wide variety of restoring forcesF(i.e.,F′>0), numerical calculations indicate the existence of a sequence of thresholds γ1= γ1(a, h, F)>γ2= γ2(a,h,F)>…>γk= γk(a,h,F)>…, γk→ 0, ask→ ∞. If γk>γ>γk+1, a k‐phase wave that is well described by the wave form,emerges and travels through the lattice.The goal of this series is to describe the emergence and calculate some properties of these wave forms. In Part I the authors first consider the case whereF(x)=ex(i.e., Toda forces) buthis arbitrary, and show how to compute a basic diagnostic (seeJ(λ), formula (1.26)) for the system in terms of the solution of an associated scalar Riemann‐Hilbert problem, once a certain finite set of numbers is known. In another direction, the authors consider the case whereF(x)is restoring but arbitrary, andhis small. Here the authors prove a general result, asserting that if there exists a sufficiently ample family of traveling‐wave solutions of the doubly infinite lattice,then it is possible to construct time‐periodick‐phase wave solutions with asymptotics innof type (iii) for the driven system (i).In Part II, the authors prove that sufficiently ample families of traveling‐wave solutions of the system (iv) exist in the cases γ>γ1and γ1>γ>γ2for general restoring forcesF. In the case with Toda forces,F(x)=ex, the authors prove that suffi

ISSN:0010-3640    

DOI:10.1002/cpa.3160481102

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

摘要:

AbstractThis is the second part of a two‐part series on forced lattice vibrations in which a semi‐infinite lattice of one‐dimensional particles {xn}n≧1,is driven from one end by a particlex0. This particle undergoes a given, periodically perturbed, uniform motionx0(t) = 2at+h(yt) whereaand γ are constants andh(·) has period 2π. Results and notation from Part I are used freely and without further comment. Here the authors prove that sufficiently ample families of traveling‐wave solutions of the doubly infinite systemexist in the cases γ>γ1and γ1>γ>γ2for general restoring forcesF.In the case with Toda forces,F(x)=ex, the authors prove that sufficiently ample families of traveling‐wave solutions exist for allk, γk>γ>γk+1. By a general result proved in Part I, this implies that there exist time‐periodic solutions of the driven system (i) withk‐phase wave asymptotics innof the typewithk= 0 or 1 for generalFandkarbitrary forF(x) =ex(when

ISSN:0010-3640    

DOI:10.1002/cpa.3160481103

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

摘要:

AbstractThis is an addendum to the author's earlier paper “Floer Cohomology of Lagrangian Intersection and Pseudo‐Holomorphic Discs, I,” Comm. Pure Appl. Math. 46, 1993, pp. 949–993. The main result of this addendum extends the definition of the Floer cohomology of Lagrangian intersection to the case where the minimal Maslov number is equal to 2. ©1996 John Wiley&S

ISSN:0010-3640    

DOI:10.1002/cpa.3160481104

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160481101

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY