On asymptotic solutions of integrable wave equations

Asymptotic 'soliton train' solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker-Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

Kernel polynomials from L-orthogonal polynomials

A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤aeigenvalue problems and numerical evaluation of the nodes and weights of such quadrature rules are also considered. © 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Limitantes para os zeros de polinômios gerados por uma relação de recorrência de três termos

Pós-graduação em Matemática - IBILCE

Sobre um método assemelhado ao de Francis para a determinação de autovalores de matrizes

Pós-graduação em Matemática - IBILCE

Compressible modes in a square lid-driven cavity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)