scholarly journals Erratum: “A characterization of causal automorphisms by wave equations” [J. Math. Phys. 53, 032507 (2012)]

2013 ◽  
Vol 54 (7) ◽  
pp. 079901 ◽  
Author(s):  
Min Kyu Kim ◽  
Do-Hyung Kim
Keyword(s):  
Wave Equations ◽  
Math Phys

scholarly journals Amplitude Recovery and Deconvolution of Chirp and Boomer Data for Marine Geology and Offshore Engineering

Energies ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5704
Author(s):  
Eleonora Denich ◽  
Aldo Vesnaver ◽  
Luca Baradello
Keyword(s):  
Wave Equations ◽  
Real Data ◽  
Image Resolution ◽  
Source Spectrum ◽  
Marine Geology ◽  
Data Types ◽  
Full Waveform ◽  
Source Signal ◽  
Geological Formations

The processing of Chirp data is limited by the usual recording of the signal envelope, which enhances its immediate visibility but prevents applying methods based on wave equations. This is normally not the case for Boomer data. However, both systems are monochannel instruments, which cannot estimate properly the propagation velocity of the signal in the rocks. In this paper, we present two theorems: the first one links the Chirp or Boomer source spectrum with an expected amplitude decay curve; the second one defines conditions for the deconvolution stability of the enveloped Boomer signal when the full waveform of the source signal is known. In this way, we can jointly process and integrate heterogeneous surveys including both data types. We validated the proposed algorithms by applying them to synthetic and real data. The presented tools can improve the image resolution and the characterization of geological formations in marine surveys by reflectivity anomalies, which are distorted by standard equalization methods.

ON BOUNDARY CONDITIONS FOR FIRST-ORDER SYMMETRIC HYPERBOLIC SYSTEMS WITH CONSTRAINTS

2013 ◽  
Vol 10 (04) ◽  
pp. 725-734 ◽  
Author(s):  
NICOLAE TARFULEA
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
First Order ◽  
The Cauchy Problem ◽  
Initial Boundary Value ◽  
Well Posed

The Cauchy problem for many first-order symmetric hyperbolic (FOSH) systems is constraint preserving, i.e. the solution satisfies certain spatial differential constraints whenever the initial data does. Frequently, artificial space cut-offs are performed for such evolution systems, usually out of the necessity for finite computational domains. However, it may easily happen that boundary conditions at the artificial boundary for such a system lead to an initial boundary value problem which, while well-posed, does not preserve the constraints. Here we consider the problem of finding constraint-preserving boundary conditions for constrained FOSH systems in the well-posed class of maximal non-negative boundary conditions. Based on a characterization of maximal non-negative boundary conditions, we discuss a systematic technique for finding such boundary conditions that preserve the constraints, pending that the constraints satisfy a FOSH system themselves. We exemplify this technique by analyzing a system of wave equations in a first-order formulation subject to divergence constraints.

scholarly journals Approximate boundary synchronization by groups for a coupled system of wave equations with coupled Robin boundary conditions

2021 ◽  
Author(s):  
Ta-Tsien Li ◽  
Bopeng Rao
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Coupled System ◽  
Algebraic Characterization ◽  
Robin Boundary Conditions ◽  
Boundary Controllability ◽  
Boundary Controls ◽  
Robin Boundary

In this paper, we first give an algebraic characterization of uniqueness of continuation for a coupled system of wave equations with coupled Robin boundary conditions. Then, the approximate boundary controllability and the approximate boundary synchronization by groups for a coupled system of wave equations with coupled Robin boundary controls are developed around this fundamental characterization.

scholarly journals Curvilinear optical fibre waveguide: characterization of bound modes and radiative field

1989 ◽  
Vol 425 (1868) ◽  
pp. 1-16 ◽  
Keyword(s):  
Optical Fibre ◽  
Optical Waveguides ◽  
Wave Equations ◽  
Propagation Constant ◽  
Three Dimensional ◽  
Current Method ◽  
Electromagnetic Current ◽  
Single Plane ◽  
Radiation Losses

Optical waveguides have assumed major importance, not only in optoelectronic applications but also, quite recently, in a study of fundamental physical properties of materials. The propagation characteristics of linear optical waveguides, and to a lesser extent those of waveguides curved in a single plane, are well understood. However, optical waveguides having three-dimensional curvature, for example the helical waveguide, have been proposed and fabricated and an analysis of its properties is essential. In this paper the scalar wave equations for a three-dimensionally curved optical fibre are solved analytically and boundary conditions are applied to the curved core-cladding interface. An asymptotic formula for computing the propagation constant is proposed and the effects of curvilinearity on the characterization of the bound modes are discussed. By using the equivalent fictitious electromagnetic current method, the far radiative field is established and expressions for the radiation losses for various modes are derived.

On the domain characterization of fractional powers of certain operator matrices generating analytic semigroups

2003 ◽  
Vol 40 (3) ◽  
pp. 327-340
Author(s):  
András Bátkai
Keyword(s):  
Wave Equations ◽  
Analytic Semigroups ◽  
Operator Matrices ◽  
Fractional Powers ◽  
Semilinear Wave Equations ◽  
Equations With Delay

We characterize the domains of fractional powers of some operator matrices generating analytic semigroups. The results are applied to wave equations with delay and semilinear wave equations.

Short wave limit of the Novikov equation and its integrable semi-discretizations

2021 ◽  
Author(s):  
Ruyun Ma ◽  
Yujuan Zhang ◽  
Na Xiong ◽  
Bao-Feng Feng
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Short Wave ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Special Cases ◽  
Two Component ◽  
Novikov Equation ◽  
Wave Limit ◽  
Math Phys

Abstract In this paper, we are concerned with one of the generalized short wave equations proposed by Hone et al. (Lett. Math. Phys 108 927 (2018)). We show that the derivative form of this equation can be viewed as a short wave limit of the Novikov (sw-Novikov) equation. Furthermore, this generalized short wave equation and its derivative form are found to be connected to period 3 reduction of two-dimensional CKP(BKP)-Toda hierarchy, same as the short wave limit of the Depasperis-Procesi (sw-DP) equation. We propose a two-component short wave equation which contain the sw-Novikov equation and sw-DP equation as two special cases. As a main result, we construct two types of integrable semi-discretizations via Hirota’s bilinear method and provide multi-soliton solution to the semi-discrete sw-Novikov equation.

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