Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Lax Pair (2)
- Solitons (2)
- Sturm-Liouville operators (2)
- Anharmonic oscillator (1)
- Asymptotics (1)
-
- Conformal Invariants (1)
- Couette flow (1)
- Crawley p group (1)
- Dean flow (1)
- Fluid dynamics (1)
- Instability (1)
- Integrable Systems (1)
- Integrable systems (1)
- Inverse Scattering (1)
- Jost function (1)
- Matched asymptotic expansions (1)
- Minimal modules (1)
- Negatons (1)
- Peakons (1)
- Perturbative expansion (1)
- Positons (1)
- Resonance (1)
- Schwarz Derivative (1)
- Torsion-free Crawley groups (1)
- Valuation domains (1)
- Volterra kernels. (1)
- Volterra series (1)
- Publication
Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Self And On-Selfadjoint Sturm-Liouville Operators With Exponentially Decaying Potentials, Alain Kerouanton
Self And On-Selfadjoint Sturm-Liouville Operators With Exponentially Decaying Potentials, Alain Kerouanton
Doctoral
In this thesis we investigate the properties of a class of linear differential operators known as Sturm-Liouville operators. Sturm-Liouville operators arise from differential equations of the form - y”+q(x)y = λy, where q is known as the potential and λ is a spectral parameter. This differential equation has been of great importance in mathematics and physics alike. We allow the potential to be real or complex valued and assume that q satisfies |q(x)|≤ce-ax, x≥0, where a >0 and c > 0. We first give a brief account of the mathematical background we will be using and then proceed to give a …
Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov
Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov
Articles
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.
On Torsion-Free Crawley Groups, Brendan Goldsmith, A. L. S. Corner, R. Gobel
On Torsion-Free Crawley Groups, Brendan Goldsmith, A. L. S. Corner, R. Gobel
Articles
The notion of a Crawley p-group is well known in Abelian group theory. In this present work, a corresponding concept is introduced for torsion-free groups. The principal result, which uses the set-theoretic notions of the diamond and Martin’s axiom, establishes an independence result for N1-free Crawley groups.
Minimal Modules Over Valuation Domains, Brendan Goldsmith, P. Zanardo
Minimal Modules Over Valuation Domains, Brendan Goldsmith, P. Zanardo
Articles
Let R be a valuation domain. We say that a torsion-free R-module is minimal if it is isomorphic to all its submodules of finite index. Here, the usual concept of finite index for groups is replaced by the more appropriate (for module theory) definition: a submodule H of the module G is said to be of finite index in G if the quotient G/H is a finitely presented torsion module. We investigate minimality in various settings and show inter alia that over a maximal valuation domain, all torsion-free modules are minimal. Constructions of non-minimal modules are given by utilizing realization …
An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
Articles
Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system and are universal for a given system. The anharmonic oscillator is chosen as an example and is discussed for different choices of its physical parameters. It is shown that the typical approach for the determination of the Volterra Series representation is not valid for the important case when the nonlinear system exhibits oscillatory behaviour and the input has a pole …
On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov
On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov
Articles
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.
Zeros Of The Jost Function For A Class Of Exponentially Decaying Potentials, Daphne Gilbert, Alain Kerouanton
Zeros Of The Jost Function For A Class Of Exponentially Decaying Potentials, Daphne Gilbert, Alain Kerouanton
Articles
We investigate the properties of a series representing the Jost solution for the differential equation $-y''+q(x)y=lambda y$, $x geq 0$, $q in mathrm{L}({mathbb{R}}^{+})$. Sufficient conditions are determined on the real or complex-valued potential $q$ for the series to converge and bounds are obtained for the sets of eigenvalues, resonances and spectral singularities associated with a corresponding class of Sturm-Liouville operators. In this paper, we restrict our investigations to the class of potentials $q$ satisfying $|q(x)| leq ce^{-ax}$, $x geq 0$, for some $a>0$ and $c$ greator than 0.
Asymptotic Methods In The Spectral Analysis Of Sturm-Liouville Operators, Daphne Gilbert
Asymptotic Methods In The Spectral Analysis Of Sturm-Liouville Operators, Daphne Gilbert
Articles
Gilbert, D.: Asymptotic Methods in the Spectral Analysis of Sturm-Lioville Operators.Sturm-Liouville theory : Past and Present, 2005, pp 121-136.
The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom
The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom
Articles
The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. Neutral curves associated with each instability can be constructed but it has been suggested that these curves do not cross but rather posses `kinks'. Our work is based in the small gap, large wavenumber limit and considers the simultaneous onset of Taylor …