POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

Some Travelling Wave Solutions of KdV-Burgers Equation

In this paper we study the extended Tanh method to obtain some exact solutions of KdV-Burgers equation. The principle of the Tanh method has been explained and then apply to the nonlinear KdV- Burgers evolution equation. A finnite power series in tanh is considered as an ansatz and the symbolic computational system is used to obtain solution of that nonlinear evolution equation. The obtained solutions are all travelling wave solutions.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Protomers: formation, separation and characterization via travelling wave ion mobility mass spectrometry

Travelling wave ion mobility mass spectrometry (TWIM-MS) with post-TWIM and pre-TWIM collision-induced dissociation (CID) experiments were used to form, separate and characterize protomers sampled directly from solutions or generated in the gas phase via CID. When in solution equilibria, these species were transferred to the gas phase via electrospray ionization, and then separated by TWIM-MS. CID performed after TWIM separation (post-TWIM) allowed the characterization of both protomers via structurally diagnostic fragments. Protonated aniline (1) sampled from solution was found to be constituted of a ca. 5:1 mixture of two gaseous protomers, that is, the N-protonated (1a) and ring protonated (1b) molecules, respectively. When dissociated, 1a nearly exclusively loses NH3, whereas 1b displays a much diverse set of fragments. When formed via CID, varying populations of 1a and 1b were detected. Two co-existing protomers of two isomeric porphyrins were also separated and characterized via post-TWIM CID. A deprotonated porphyrin sampled from a basic methanolic solution was found to be constituted predominantly of the protomer arising from deprotonation at the carboxyl group, which dissociates promptly by CO2 loss, but a CID-resistant protomer arising from deprotonation at a porphyrinic ring NH was also detected and characterized. The doubly deprotonated porphyrin was found to be constituted predominantly of a single protomer arising from deprotonation of two carboxyl groups. Copyright (C) 2012 John Wiley & Sons, Ltd.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Travelling waves in a model of species migration

A model of species migration is presented which takes the form of a reaction-diffusion system. We consider special limits of this model in which we demonstrate the existence of travelling wave solutions. These solutions can be used to describe the migration of cells, bacteria, and some organisms. © 2000 Elsevier Science Ltd. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

On the energy transported by exact plane gravitational-wave solutions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Entropic information for travelling solitons in Lorentz and CPT breaking systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Resolution of isomeric multi-ruthenated porphyrins by travelling wave ion mobility mass spectrometry

The ability of travelling wave ion mobility mass spectrometry (TWIM-MS) to resolve cationic meta/para and cis/trans isomers of mono-, di-, tri- and tetra-ruthenated supramolecular porphyrins was investigated. All meta isomers were found to be more compact than the para isomers and therefore mixtures of all isomeric pairs could be properly resolved with baseline or close to baseline peak-to-peak resolution (Rp-p). Di-substituted cis/trans isomers were found, however, to present very similar drift times and could not be resolved. N-2 and CO2 were tested as the drift gas, and similar a but considerably better values of R-p and Rp-p were always observed for CO2. Copyright (C) 2012 John Wiley & Sons, Ltd.

Exploring the coordination chemistry of isomerizable terpyridine derivatives for successful analyses of cis and trans isomers by travelling wave ion mobility mass spectrometry

The photochemical cis-trans isomerization of the 4-{4-[2-(pyridin-4-yl)ethenyl]phenyl}-2,2': 6',2''-terpyridine ligand (vpytpy) was investigated by UV-vis, NMR and TWIM-MS. Ion mobility mass spectrometry was performed pursuing the quantification of the isomeric composition during photolysis, however an in-source trans-to-cis isomerization process was observed. In order to overcome this inherent phenomenon, the isomerization of the vpytpy species was suppressed by complexation, reacting with iron(II) ions, and forming the [Fe(vpytpy)(2)](2+) complex. The strategy of "freezing" the cis-trans isomerizable ligand at a given geometric conformation was effective, preventing further isomerization, thus allowing the distinction of each one of the isomers in the photolysed mixture. In addition, the experimental drift times were related to the calculated surface areas of the three possible cis-cis, cis-trans and trans-trans iron(II) complex isomers. The stabilization of the ligand in a given conformation also allows us to obtain the cis-cis and cis-trans complexes exhibiting the ligand in the metastable cis-conformation, as well as in the thermodynamically stable trans-conformation.