Convergence to Normal Forms of Integrable PDEs
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03661-8
Abstract: In an infinite dimensional Hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields. We prove that one can… read more here.
Keywords: integrable pdes; convergence normal; normal form; forms integrable ... See more keywords
Comparing the direct normal form and multiple scales methods through frequency detuning
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-018-4534-1
Abstract: Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics.… read more here.
Keywords: normal form; form multiple; direct normal; multiple scales ... See more keywords
Nonlinear Oscillations of a Spring Pendulum at the 1:1:2 Resonance by Normal Form Methods
Sign Up to like & getrecommendations! Published in 2020 at "Mathematics in Computer Science"
DOI: 10.1007/s11786-019-00427-2
Abstract: The object of this research is the process of small oscillations of a three-dimensional elastic pendulum, tuned to a 1:1:2 resonance to vertical and horizontal oscillations. The purpose is to develop a symbolic algorithm for… read more here.
Keywords: mathematics; normal form; resonance; method ... See more keywords
Forced Nonlinear vibration and bifurcation analysis of circular cylindrical nanocomposite shells using the normal form
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Non-linear Mechanics"
DOI: 10.1016/j.ijnonlinmec.2021.103733
Abstract: Abstract The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical… read more here.
Keywords: vibration; normal form; nonlinear vibration; using normal ... See more keywords
Versal normal form for nonsemisimple singularities
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.03.039
Abstract: Abstract The theory of versal normal form has been playing a role in normal form since the introduction of the concept by V.I. Arnol'd in [1] , [2] . But there has been no systematic… read more here.
Keywords: form; nonsemisimple singularities; versal normal; normal form ... See more keywords
Normal form of nonlinear oscillator model relevant to spin-torque nano-oscillator theory
Sign Up to like & getrecommendations! Published in 2018 at "Physica B: Condensed Matter"
DOI: 10.1016/j.physb.2017.10.021
Abstract: Abstract We introduce a normal form for the equation which describes nonlinear oscillations of spin-torque nano-oscillators (STNO). The general form of the equation might be reduced to the equation for STNO with uniformly magnetized free… read more here.
Keywords: normal form; frequency; oscillator; equation ... See more keywords
Normal forms of C∞ vector fields based on the renormalization group
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0031043
Abstract: The normal form theory for polynomial vector fields is extended to those for C∞ vector fields vanishing at the origin. Explicit formulas for the C∞ normal form and the near identity transformation that brings a… read more here.
Keywords: normal forms; renormalization group; vector fields; normal form ... See more keywords
Enumeration of subdifferentials of piecewise linear functions with abs-normal form
Sign Up to like & getrecommendations! Published in 2018 at "Optimization Methods and Software"
DOI: 10.1080/10556788.2018.1458848
Abstract: The directional derivatives of a piecewise smooth function at a given point can be computed with Griewank's absolute normal form (ANF). When the given point is a non-differentiable point, the resulting derivative by ordinary algorithmic… read more here.
Keywords: enumeration subdifferentials; piecewise linear; point; normal form ... See more keywords
Cooperative Semiglobal Robust Output Regulation of Non-Introspective Nonlinear Agents With Partial Normal Form and State-Dependent High-Frequency Gain
Sign Up to like & getrecommendations! Published in 2019 at "IEEE Transactions on Control of Network Systems"
DOI: 10.1109/tcns.2018.2834309
Abstract: This paper investigates cooperative semig-lobal robust output regulation problem for a class of non-introspective nonlinear multiagent systems. Each agent of this class is allowed to have a partial normal form, instead of only the conventional… read more here.
Keywords: robust output; gain; normal form; output ... See more keywords
A normal form for frequency combs and localized states in Kerr-Gires-Tournois interferometers.
Sign Up to like & getrecommendations! Published in 2022 at "Optics letters"
DOI: 10.1364/ol.457777
Abstract: We elucidate the mechanisms that underlay the formation of temporal localized states and frequency combs in vertical external-cavity Kerr-Gires-Tournois interferometers. We reduce our first-principles model based upon delay algebraic equations to a minimal pattern formation… read more here.
Keywords: tournois interferometers; frequency combs; localized states; gires tournois ... See more keywords
Normal form of O(2) Hopf bifurcation in a model of a nonlinear optical system with diffraction and delay
Sign Up to like & getrecommendations! Published in 2017 at "Electronic Journal of Qualitative Theory of Differential Equations"
DOI: 10.14232/ejqtde.2017.1.50
Abstract: In this paper we construct an O(2)-equivariant Hopf bifurcation normal form for a model of a nonlinear optical system with delay and diffraction in the feedback loop whose dynamics is governed by a system of… read more here.
Keywords: model nonlinear; system; normal form; form ... See more keywords