Negaton and Positon solutions of the soliton equation with self-consistent sources

The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for $N$-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund transformation between two KdV equations with different degrees of sources and enable us to construct more general solutions with $N$ arbitrary $t$-dependent functions. By taking the special $t$-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of KdVES. Some properties of these solutions are discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge

Propagating EUV disturbances in the solar corona : two-wavelength observations

Quasi-periodic EUV disturbances simultaneously observed in 171 Å and 195 Å TRACE bandpasses propagating outwardly in a fan-like magnetic structure of a coronal active region are analysed. Time series of disturbances observed in the different bandpasses have a relatively high correlation coefficient (up to about 0.7). The correlation has a tendency to decrease with distance along the structure: this is consistent with an interpretation of the disturbances in terms of parallel-propagating slow magnetoacoustic waves. The wavelet analysis does not show a significant difference between waves observed in different bandpasses. Periodic patterns of two distinct periods: 2-3 min and 5-8 min are detected in both bandpasses, existing simultaneously and at the same distance along the loop, suggesting the nonlinear generation of the second harmonics

Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim

In classical Kaluza-Klein theory, with compactified extra dimensions and without scalar field, the rest mass as well as the electric charge of test particles are constants of motion. We show that in the case of a large extra dimension this is no longer so. We propose the Hamilton-Jacobi formalism, instead of the geodesic equation, for the study of test particles moving in a five-dimensional background metric. This formalism has a number of advantages: (i) it provides a clear and invariant definition of rest mass, without the ambiguities associated with the choice of the parameters used along the motion in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the discussion, and (iii) we avoid the difficulties associated with the "splitting" of the geodesic equation. For particles moving in a general 5D metric, we show how the effective rest mass, as measured by an observer in 4D, varies as a consequence of the large extra dimension. Also, the fifth component of the momentum changes along the motion. This component can be identified with the electric charge of test particles. With this interpretation, both the rest mass and the charge vary along the trajectory. The constant of motion is now a combination of these quantities. We study the cosmological variations of charge and rest mass in a five-dimensional bulk metric which is used to embed the standard k = 0 FRW universes. The time variations in the fine structure "constant" and the Thomson cross section are also discussed.Comment: V2: References added, discussion extended. V3 is identical to V2, references updated. To appear in General Relativity and Gravitatio

Integrable dispersionless KdV hierarchy with sources

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge

Effective spacetime from multi-dimensional gravity

We study the effective spacetimes in lower dimensions that can be extracted from a multidimensional generalization of the Schwarzschild-Tangherlini spacetimes derived by Fadeev, Ivashchuk and Melnikov ({\it Phys. Lett,} {\bf A 161} (1991) 98). The higher-dimensional spacetime has $D = (4 + n + m)$ dimensions, where $n$ and $m$ are the number of "internal" and "external" extra dimensions, respectively. We analyze the effective $(4 + n)$ spacetime obtained after dimensional reduction of the $m$ external dimensions. We find that when the $m$ extra dimensions are compact (i) the physics in lower dimensions is independent of $m$ and the character of the singularities in higher dimensions, and (ii) the total gravitational mass $M$ of the effective matter distribution is less than the Schwarzshild mass. In contrast, when the $m$ extra dimensions are large this is not so; the physics in $(4 + n)$ does explicitly depend on $m$, as well as on the nature of the singularities in high dimensions, and the mass of the effective matter distribution (with the exception of wormhole-like distributions) is bigger than the Schwarzshild mass. These results may be relevant to observations for an experimental/observational test of the theory.Comment: A typo in Eq. (24) is fixe

The Solutions of the NLS Equations with Self-Consistent Sources

We construct the generalized Darboux transformation with arbitrary functions in time $t$ for the AKNS equation with self-consistent sources (AKNSESCS) which, in contrast with the Darboux transformation for the AKNS equation, provides a non-auto-B\"{a}cklund transformation between two AKNSESCSs with different degrees of sources. The formula for N-times repeated generalized Darboux transformation is proposed. By reduction the generalized Darboux transformation with arbitrary functions in time $t$ for the Nonlinear Schr\"{o}dinger equation with self-consistent sources (NLSESCS) is obtained and enables us to find the dark soliton, bright soliton and positon solutions for NLS$^{+}$ESCS and NLS$^{-}$ESCS. The properties of these solution are analyzed.Comment: 24 pages, 3 figures, to appear in Journal of Physics A: Mathematical and Genera

Genetic variation in Southern USA rice genotypes for seedling salinity tolerance

The success of a rice breeding program in developing salt tolerant varieties depends on genetic variation and the salt stress response of adapted and donor rice germplasm. In this study, we used a combination of morphological and physiological traits in multivariate analyses to elucidate the phenotypic and genetic variation in salinity tolerance of thirty Southern USA rice genotypes, along with nineteen donor genotypes with varying degrees of tolerance. Significant genotypic variation and correlations were found among the salt injury score (SIS), ion leakage, chlorophyll reduction, shoot length reduction, shoot K+ concentration, and shoot Na+/K+ ratio. Using these parameters, the combined methods of cluster analysis and discriminant analysis validated the salinity response of known genotypes and classified most of the USA varieties into sensitive groups, except for three and seven varieties placed in the tolerant and moderately tolerant groups, respectively. Discriminant function and MANOVA delineated the differences in tolerance and suggested no differences between sensitive and highly sensitive groups. DNA profiling using simple sequence repeat markers showed narrow genetic diversity among USA genotypes. However, the overall genetic clustering was mostly due to subspecies and grain type differentiation and not by varietal grouping based on salinity tolerance. Among the donor genotypes, Nona Bokra, Pokkali, and its derived breeding lines remained the donors of choice for improving salinity tolerance during the seedling stage. However, due to undesirable agronomic attributes and photosensitivity of these donors, alternative genotypes such as TCCP266, Geumgangbyeo, and R609 are recommended as useful and novel sources of salinity tolerance for USA rice breeding programs

Generalized Darboux transformations for the KP equation with self-consistent sources

The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we construct the generalized binary Darboux transformation with arbitrary functions in time $t$ for the KPESCS which, in contrast with the binary Darboux transformation of the KP equation, provides a non-auto-B\"{a}cklund transformation between two KPESCSs with different degrees. The formula for N-times repeated generalized binary Darboux transformation is proposed and enables us to find the N-soliton solution and lump solution as well as some other solutions of the KPESCS.Comment: 20 pages, no figure

Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systems

We study thermally activated, low temperature equilibrium dynamics of elastic systems pinned by disorder using one loop functional renormalization group (FRG). Through a series of increasingly complete approximations, we investigate how the field theory reveals the glassy nature of the dynamics, in particular divergent barriers and barrier distributions controling the spectrum of relaxation times. A naive single relaxation time approximation for each wavevector is found to be unsatisfactory. A second approximation based on a random friction model, yields a size (L) dependent log-normal distribution of relaxation times (mean barriers ~L^\theta and variance ~ L^{\theta/2}) and a procedure to estimate dynamical scaling functions. Finally, we study the full structure of the running dynamical effective action within the field theory. We find that relaxation time distributions are non-trivial (broad but not log-normal) and encoded in a closed hierarchy of FRG equations. A thermal boundary layer ansatz (TBLA) appears as a consistent solution. It extends the one discovered in the statics which was shown to embody droplet thermal fluctuations. Although perturbative control remains a challenge, the structure of the dynamical TBLA which encodes barrier distributions opens the way for deeper understanding of the field theory approach to glasses