Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise.
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
Solution explicite du problème de Cauchy pour un opérateur hyperbolique à caractéristiques non régulières
Solution of a spectral problem for the curl operator on a cylinder.
Solution of the Dirichlet problem for the Laplace equation
For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.
Solutions classification to the extended reduced Ostrovsky equation.
Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier
2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.We give here examples of equations of type (1) ∂tt2 y -p(t, Dx) y = 0, where p is a singular pseudo-differential operator with regular global solutions when the Cauchy data are regular, t ∈ R, x ∈ R5.
Solutions in Gevrey spaces of partial differential equations with constant coefficients
Si dà una condizione sufficiente per la esistenza di una soluzione in uno spazio di Gevrey , razionale , , di una equazione lineare a derivate parziali a coefficienti costanti , quando . La dimostrazione completa dei risultati ottenuti è contenuta in una nota dell’autore in corso di pubblicazione su "Astérisque".
Solutions of Analytical Systems of Partial Differential Equations
In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).
Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis
In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure...
Solutions to some nonlinear PDE's in the form of Laplace type integrals
A nonlinear equation in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of Char P, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.
Solutions to three-dimensional Navier-Stokes equations for incompressible fluids.
Solving initial-boundary value problems for coupled systems of partial differential equations
Some exact Solutions of the Korteweg-de Vries Equation with Variable Coefficients
Some Fractional Extensions of the Temperature Field Problem in Oil Strata
This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed...
Some Linear Elliptic Selfsimilar Equations with Whirl-Like Solutions.
Some properties of the Feynman-Kac functional.
Some Remarks on Transmutation, Scattering Theory, and Special Functions.
Some remarks on two-scale convergence and periodic unfolding
The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization...
Some solutions for a class of singular equations
In this paper we obtain all solutions which depend only on for a class of partial differential equations of higher order with singular coefficients.