Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations

In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon and cuspon solutions. One of the considered GCH equations supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. The second equation does not support singular traveling waves and the last one supports four-segmented, non-smooth $M$-wave solutions. Moreover, smooth traveling waves of the three GCH equations are considered. Here, we use a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of their traveling-wave equations, corresponding to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding GCH equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. We also show the traveling wave nature of these pulse and front solutions to the GCH NLPDEs

Regular and Singular Pulse and Front Solutions and Possible Isochronous Behavior in the Short-Pulse Equation: Phase-Plane, Multi-Infinite Series and Variational Approaches

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively of the original PDEs. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the SPE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized SPE equations considered here, the results obtained are both new and timely.Comment: accepted for publication in Communications in Nonlinear Science and Numerical Simulatio

Charge carrier mobility in an organic-inorganic hybrid nanocomposite

Organic-inorganic hybrid materials are media for electronic and optoelectronic applications. We present a study of the electronic transport in such a modelnanoparticle-sensitizedhybridorganic-inorganic photorefractive host system, consisting of poly(N-vinylcarbazole) doped with quantum dots of cadmium sulfide, using standard time-of-flight techniques. The photocurrent transients exhibit features typical of dispersive transport in an amorphous semiconductor. The hole mobility depends strongly on the electric field and temperature indicating Poole–Frenkel-like activated hopping transport; a thickness dependence of the mobility is observed. The presence of nanoparticles does not lead to increased trapping of holes. Conversely, a surprising result is observed: the mobility actually increases with the increase of nanoparticle concentration even though it is well below the percolation limit.This study was supported by a NSF, DMR Solid State and Polymer Chemistry Grant No. DMR0075867. Partial support by a Defense Research Initiative on Nanotechnology (DURINT), Contract No. F496200110358, through the Directorate of Chemistry and Life Sciences of the Air Force Office of Scientific Research is also acknowledged

Anomaly mediated supersymmetry breaking and its test in linear colliders

Signatures of anomaly mediated supersymmetry breaking in linear colliders are briefly reviewed after presenting an outline of the theoretical framework. A unique and distinct feature of a large class of models of this type is a winolike chargino which is very closely degenerate in mass with the lightest neutralino. The very slow decay of this chargino results in a heavily ionizing charged track and one soft charged pion with a characteristic momentum distribution, leading to unique signals in linear colliders which are essentially free of background. The determination of chargino and slepton masses from such events is a distinctly interesting possibility.Comment: 15 pages, LaTex, 4 PS figures, ws-mpla.cls file included. One reference added. To appear as a Brief Review in Modern Physics Letters

Isgur-Wise Function for Heavy Light Mesons in D dimensional Potential Model

We report results of a potential model for mesons in D space-time dimension developed by considering the quark-antiquark potential of Nambu-Goto strings. With this wave function, we have studied Isgur-Wise function for heavy-light mesons and its derivatives like slope and curvature. The dimensional dependence of our results and a comparative study with the results of 3+1 dimensional QCD are also reported.Comment: 11 pages, 4 figure

Can the clustered dark matter and the smooth dark energy arise from the same scalar field ?

Cosmological observations suggest the existence of two different kinds of energy densities dominating at small ($\lesssim 500$ Mpc) and large ($\gtrsim 1000$ Mpc) scales. The dark matter component, which dominates at small scales, contributes $\Omega_m \approx 0.35$ and has an equation of state $p=0$ while the dark energy component, which dominates at large scales, contributes $\Omega_V \approx 0.65$ and has an equation of state $p\simeq -\rho$. It is usual to postulate wimps for the first component and some form of scalar field or cosmological constant for the second component. We explore the possibility of a scalar field with a Lagrangian L =- V(\phi) \sqrt{1 - \del^i \phi \del_i \phi} acting as {\it both} clustered dark matter and smoother dark energy and having a scale dependent equation of state. This model predicts a relation between the ratio $r = \rho_V/\rho_{\rm DM}$ of the energy densities of the two dark components and expansion rate $n$ of the universe (with $a(t) \propto t^n$) in the form $n = (2/3) (1+r)$. For $r \approx 2$, we get $n \approx 2$ which is consistent with observations.Comment: Revised to match the published version. Minor changes and a reference adde

A theoretician's analysis of the supernova data and the limitations in determining the nature of dark energy

Current cosmological observations show a strong signature of the existence of a dark energy component with negative pressure. The most obvious candidate for this dark energy is the cosmological constant (with the equation of state w_X=p/\rho=-1), which, however, raises several theoretical difficulties. This has led to models for dark energy component which evolves with time. We discuss certain questions related to the determination of the nature of dark energy component from observations of high redshift supernova. The main results of our analysis are: (i) Even if the precise value of w_X is known from observations, it is not possible to determine the nature of the unknown dark energy source using only kinematical and geometrical measurements. We have given explicit examples to show that different types of sources can give rise to a given w_X. (ii) Although the full data set of supernova observations (which are currently available) strongly rule out models without dark energy, the high (z>0.25) and low (z<0.25) redshift data sets, individually, admit decelerating models with zero dark energy. Any possible evolution in the absolute magnitude of the supernovae, if detected, might allow the decelerating models to be consistent with the data. (iii) We have introduced two parameters, which can be obtained entirely from theory, to study the sensitivity of the luminosity distance on w_X. Using these two parameters, we have argued that although one can determine the present value of w_X accurately from the data, one cannot constrain the evolution of w_X.Comment: Revised versio