scholarly journals Asymptotic analysis for non-local curvature flows for plane curves with a general rotation number

2021 ◽  
Vol 3 (6) ◽  
pp. 1-26
Author(s):  
Takeyuki Nagasawa ◽  
◽  
Kohei Nakamura
Keyword(s):  
Asymptotic Analysis ◽  
Rotation Number ◽  
Plane Curves ◽  
Local Curvature ◽  
General Rotation ◽  
Non Local

scholarly journals Rational solutions of the defocusing non-local nonlinear Schrödinger equation: asymptotic analysis and soliton interactions

2021 ◽  
Vol 477 (2254) ◽  
Author(s):  
Tao Xu ◽  
Lingling Li ◽  
Min Li ◽  
Chunxia Li ◽  
Xuefeng Zhang
Keyword(s):  
Schrödinger Equation ◽  
Asymptotic Analysis ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Algebraic Curves ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Soliton Interactions ◽  
Nonlinear Schrödinger ◽  
Non Local

In this paper, we obtain the N th-order rational solutions for the defocusing non-local nonlinear Schrödinger equation by the Darboux transformation and some limit technique. Then, via an improved asymptotic analysis method relying on the balance between different algebraic terms, we derive the explicit expressions of all asymptotic solitons of the rational solutions with the order 1 ≤ N ≤ 4 . It turns out that the asymptotic solitons are localized in the straight lines or algebraic curves, and the exact solutions approach the curved asymptotic solitons with a slower rate than the straight ones. Moreover, we find that all the rational solutions exhibit just five different types of soliton interactions, and the interacting solitons are divided into two halves with each having the same amplitudes. Particularly for the curved asymptotic solitons, there may exist a slight difference for their velocities between at t and − t with certain parametric conditions. In addition, we reveal that the soliton interactions in the rational solutions with N ≥ 2 are stronger than those in the exponential and exponential-and-rational solutions.

scholarly journals Non-local curvature and Gauss–Bonnet cosmologies by Noether symmetries

2020 ◽  
Vol 135 (12) ◽  
Author(s):  
Francesco Bajardi ◽  
Salvatore Capozziello ◽  
Daniele Vernieri
Keyword(s):  
Noether Symmetries ◽  
Field Equations ◽  
Local Curvature ◽  
Symmetry Approach ◽  
Local Gravity ◽  
Cosmological Solutions ◽  
Related Point ◽  
Functional Forms ◽  
Non Local ◽  
Scalar Invariants

AbstractNon-local gravity cosmologies are considered under the standard of Noether symmetry approach. In particular, we focus on non-local theories whose gravitational actions depend on curvature and Gauss–Bonnet scalar invariants. Specific functional forms of the related point-like Lagrangians are selected by Noether symmetries, and we solve the corresponding field equations finding out exact cosmological solutions.

scholarly journals On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity

2016 ◽  
Vol 19 (05) ◽  
pp. 1650035 ◽  
Author(s):  
Indranil Chowdhury ◽  
Prosenjit Roy
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Fractional Laplacian ◽  
Elliptic Problems ◽  
Weighted Estimate ◽  
Dirichlet Problems ◽  
Nonlocal Equations ◽  
Cylindrical Domains ◽  
Non Local ◽  
Second Order Elliptic Problems

The paper is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second-order elliptic problems by Chipot and Rougirel in [On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math. 4(1) (2002) 15–44], where the force functions are considered on the cross-section of domains, we prove the non-local counterpart of their result.Recently in [Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89(1–2) (2014) 21–35] Yeressian established a weighted estimate for solutions of non-local Dirichlet problems which exhibit the asymptotic behavior. The case when [Formula: see text] was also treated as an example to show how the weighted estimate might be used to achieve the asymptotic behavior. In this paper, we extend this result to each order between [Formula: see text] and [Formula: see text].

Local and non-local curvature approximation: a new asymptotic theory for wave scattering

2003 ◽  
Vol 13 (4) ◽  
pp. 321-337 ◽  
Author(s):  
Tanos Elfouhaily ◽  
Stephan Guignard ◽  
Ra'id Awadallah ◽  
Donald R Thompson
Keyword(s):  
Wave Scattering ◽  
Asymptotic Theory ◽  
Local Curvature ◽  
Non Local ◽  
Curvature Approximation

AN AREA-PRESERVING FLOW FOR CLOSED CONVEX PLANE CURVES

2013 ◽  
Vol 24 (04) ◽  
pp. 1350029 ◽  
Author(s):  
YUEYUE MAO ◽  
SHENGLIANG PAN ◽  
YILING WANG
Keyword(s):  
Evolution Equation ◽  
American Mathematical Society ◽  
Nonlinear Problems ◽  
Local Area ◽  
Mathematical Society ◽  
Plane Curves ◽  
Curve Flow ◽  
Convex Plane ◽  
Non Local ◽  
Area Preserving

Motivated by Gage [On an area-preserving evolution equation for plane curves, in Nonlinear Problems in Geometry, ed. D. M. DeTurck, Contemporary Mathematics, Vol. 51 (American Mathematical Society, Providence, RI, 1986), pp. 51–62] and Ma–Cheng [A non-local area preserving curve flow, preprint (2009), arXiv:0907.1430v2, [math.DG]], in this paper, an area-preserving flow for convex plane curves is presented. This flow will decrease the perimeter of the evolving curve and make the curve more and more circular during the evolution process. And finally, as t goes to infinity, the limiting curve will be a finite circle in the C∞ metric.

scholarly journals Non-local curvature gravity cosmology via Noether symmetries

2022 ◽  
pp. 136907
Author(s):  
Adriano Acunzo ◽  
Francesco Bajardi ◽  
Salvatore Capozziello
Keyword(s):  
Noether Symmetries ◽  
Local Curvature ◽  
Non Local
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