General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix Riemann-Hilbert problem. We have applied these general results to the three-wave interaction system, and derived new classes of higher-order soliton and two-soliton solutions, in complement to those from our previous publication [Stud. Appl. Math. 110, 297 (2003)], where only the elementary higher-order zeros were considered. The higher-order solitons corresponding to nonelementary zeros generically describe the simultaneous breakup of a pumping wave (u(3)) into the other two components (u(1) and u(2)) and merger of u(1) and u(2) waves into the pumping u(3) wave. The two-soliton solutions corresponding to two simple zeros generically describe the breakup of the pumping u(3) wave into the u(1) and u(2) components, and the reverse process. In the nongeneric cases, these two-soliton solutions could describe the elastic interaction of the u(1) and u(2) waves, thus reproducing previous results obtained by Zakharov and Manakov [Zh. Eksp. Teor. Fiz. 69, 1654 (1975)] and Kaup [Stud. Appl. Math. 55, 9 (1976)]. (C) 2003 American Institute of Physics.

Soliton solutions for the super mKdV and sinh-Gordon hierarchy

The dressing and vertex operator formalism is emploied to study the soliton solutions of the N = I super mKdV and sinh-Gordon models. Explicit two and four vertex solutions are constructed. The relation between the soliton solutions of both models is verified. (c) 2006 Elsevier B.V. All rights reserved.

A class of soliton solutions for the N=2 super mKdV/Sinh-Gordon hierarchy

Employing Hirota's method, a class of soliton solutions for the N = 2 super mKdV equations is proposed in terms of a single Grassmann parameter. Such solutions are shown to satisfy two copies of N = 1 supersymmetric mKdV equations connected by nontrivial algebraic identities. Using the super Miura transformation, we obtain solutions of the N = 2 super KdV equations. These are shown to generalize solutions derived previously. By using them KdV/sinh-Gordon hierarchy properties we generate the solutions of the N = 2 super sinh-Gordon as well.

q-Analog of the gap equation for cuprates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Soliton parameters and chaotic sets

In this work we apply a nonperturbative approach to analyze soliton bifurcation ill the presence of surface tension, which is a reformulation of standard methods based on the reversibility properties of the system. The hypothesis is non-restrictive and the results can be extended to a much wider variety of systems. The usual idea of tracking intersections of unstable manifolds with some invariant set is again used, but reversibility plays an important role establishing in a geometrical point of view some kind of symmetry which, in a classical way, is unknown or nonexistent. Using a computer program we determine soliton solutions and also their bifurcations ill the space of parameters giving a picture of the chaotic structural distribution to phase and amplitude shift phenomena. (C) 2009 Published by Elsevier Ltd.

Negative even grade mKdV hierarchy and its soliton solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dipolar Bose-Einstein condensate soliton on a two-dimensional optical lattice

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

Evolutions of matter-wave bright soliton with spatially modulated nonlinearity

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

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

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

Symbiotic gap and semigap solitons in Bose-Einstein condensates

Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of interspecies repulsion, while the intraspecies interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intragap (with both chemical potentials falling into a single band gap) or intergap, otherwise. In the case of the intraspecies attraction, a smooth transition takes place between solitons in the semi-infinite gap, those in the first finite band gap, and semigap solitons (with one component in a band gap and the other in the semi-infinite gap).

Two-component gap solitons with linear interconversion

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

Negative Even Grade mKdV Hierarchy and its Soliton Solutions

In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra (s) over capl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method based on non zero vacua. The sub-hierarchies admiting such class of solutions are classified.

Nonzero Gap Two-Dimensional Carbon Allotrope from Porous Graphene

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Refractive index changes in photochromic SbPO4-WO3 glass by exposure to band-gap radiation

We report photoinduced photo-darkening in SbPO4-WO3 glass by exposure to 532 nm light with a power density of 143 mW/cm(2). The time of exposure was varied between 0 and 256 min following which visible photo-darkening, peaking at 850 nm was observed. Spectrophotometer measurement of absorption was performed for both treated and untreated regions of the sample. Time exposure to below band-gap light results in a single exponent Gaussian absorption function over an exceptionally wide range of wavelengths (500 nm-1600 nm), with a 1/e width of 647.5 nm. Kramers-Kronig transform of the change in the absorption indicates a negative local change in the refractive index. The dispersed refractive index change at 1550 nm, Delta n, is calculated to be similar to -5 x 10(-8). The peak absorption increases with time of exposure and the photo-darkening remains irreversible at room temperature. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.

Canopy gap colonization in the Atlantic Montane Rain Forest

Na Floresta Pluvial Atlântica Montana do Sudeste Brasileiro, foi realizado um estudo para descrever e avaliar a colonização de clareiras. A composição de clareiras foi levantada através da cobertura do solo para as espécies herbáceas enquanto que todos os indivíduos lenhosos maiores que um metro de altura foram mensurados e identificados. Também foram coletadas informações sobre a estrutura das clareiras (área da clareira, número e diâmetro das quedas), posição topográfica e vegetação circundante. Dois gêneros de Marantaceae apresentaram considerável freqüência e abundância nas clareiras. As espécies lenhosas mais freqüentes e abundantes pertenceram ao grupo não-pioneiro e as famílias mais ricas encontradas nas clareiras não diferiram quando comparado à floresta como um todo. Como para as variáveis do estrato herbáceo e da vegetação circundante, os resultados revelaram que efeitos diretos e indiretos da topografia são importantes na determinação da composição interna de clareiras por espécies lenhosas. Estes resultados sugerem que a colonização de clareiras é influenciada não apenas pelas variáveis de estrutura, mas também pela posição topográfica e pelos indivíduos pré-estabelecidos.