8,729 research outputs found
Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case
Extending previous results of Oh--Zumbrun and Johnson--Zumbrun, we show that
spectral stability implies linearized and nonlinear stability of spatially
periodic traveling-wave solutions of viscous systems of conservation laws for
systems of generic type, removing a restrictive assumption that wave speed be
constant to first order along the manifold of nearby periodic solutions.Comment: Fixed minor typo
Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev-Petviashvili Equation
In this paper, we investigate the spectral instability of periodic traveling
wave solutions of the generalized Korteweg-de Vries equation to long wavelength
transverse perturbations in the generalized Kadomtsev-Petviashvili equation. By
analyzing high and low frequency limits of the appropriate periodic Evans
function, we derive an orientation index which yields sufficient conditions for
such an instability to occur. This index is geometric in nature and applies to
arbitrary periodic traveling waves with minor smoothness and convexity
assumptions on the nonlinearity. Using the integrable structure of the ordinary
differential equation governing the traveling wave profiles, we are then able
to calculate the resulting orientation index for the elliptic function
solutions of the Korteweg-de Vries and modified Korteweg-de Vries equations.Comment: 26 pages. Sign error corrected in Lemma 3. Statement of main theorem
corrected. Exposition updated and references added
The Fraud Act 2006 : The E-crime Prosecutor’s Champion or the Creator of a New Inchoate Offence?
An analysis of whether the Fraud Act 2006 is sufficently rebust to be able to tackle the challenges of e-crimePeer reviewedFinal Accepted Versio
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