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.

Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations

For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary condition in L-2(Omega). For a dissipative nonlinearity f satisfying a suitable growth restrictions these equations define on the phase space H-0(1)(Omega) x L-2(Omega) semigroups {T-eta(t) : t >= 0} which have global attractors A(eta) eta >= 0. We show that the family {A(eta)}(eta >= 0), behaves upper and lower semi-continuously as the parameter eta tends to 0(+).

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.

Estudo analítico/numérico do problema de ablação em corpos rombudos com simetria axial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelos matemáticos e aplicações ao ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Análise de estabilidade de sistemas dinâmicos híbridos e descontínuos modelados por semigrupos:

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Teoria de estabilidade de equações diferenciais ordinárias e aplicações: modelos presa-predador e competição entre espécies

Pós-graduação em Matemática Universitária - IGCE

Estudo clássico completo do formalismo de Hamilton-Jacobi

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Description of the attainable sets of one-dimensional differential inclusions

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Soluções numéricas de Equações Diferenciais Fracionária e Ordinária para o cálculo da distribuição da concentração em um sistema de compartimento

The purpose of this work was the study of numerical methods for differential equations of fractional order and ordinary. These methods were applied to the problem of calculating the distribution of the concentration of a given substance over time in a given physical system. The two compartment model was used for representation of this system. Comparison between numerical solutions obtained were performed and, in particular, also compared with the analytical solution of this problem. Finally, estimates for the error between the solutions were calculated

Differential orthogonality: Laguerre and Hermite cases with applications

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

Differential cross sections for elastic and inelastic positronium-hydrogen-atom scattering

A time reversal symmetric regularized electron exchange model was used to elastic scattering, target elastic Ps excitations and target inelastic excitation of hydrogen in a five state coupled model. A singlet Ps-H-S-wave resonance at 4.01 eV of width 0.15 eV and a P-wave resonance at 5.08 eV of width 0.004 eV were obtained using this model. The effect on the convergence of the coupled-channel scheme due to the inclusion of the excited Ps and H states was also analyzed.

Estabilidade de pontos de equilíbrio e existência de soluções periódicas em alguns modelos bidimensionais

Pós-graduação em Matemática Universitária - IGCE