Studies in Applied Mathematics 

About: Studies in Applied Mathematics is an academic journal published by Wiley-Blackwell. The journal publishes majorly in the area(s): Nonlinear system & Partial differential equation. It has an ISSN identifier of 0022-2526. Over the lifetime, 1776 publications have been published receiving 51619 citations. The journal is also known as: MIT Journal of Mathematics and Physics.

The Inverse scattering transform fourier analysis for nonlinear problems

Abstract: A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering The form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator A comprehensive presentation of the inverse scattering method is given and general features of the solution are discussed The relationship of the scattering theory and Backlund transformations is brought out In view of the role of the dispersion relation, the comparatively simple asymptotic states, and the similarity of the method itself to Fourier transforms, this theory can be considered a natural extension of Fourier analysis to nonlinear problems

On the Boundary Condition at the Surface of a Porous Medium

Abstract: A theoretical justification is given for an empirical boundary condition proposed by Beavers and Joseph [1]. The method consists of first using a statistical approach to extend Darcy's law to non homogeneous porous medium. The limiting case of a step function distribution of permeability and porosity is then examined by boundary layer techniques, and shown to give the required boundary condition. In an Appendix, the statistical approach is checked by using it to derive Einstein's law for the viscosity of dilute suspensions.

Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

Abstract: The equation dealt with in this paper is in three dimensions. It comes from minimizing the functional which, in turn, comes from an approximation to the Hartree-Fock theory of a plasma. It describes an electron trapped in its own hole. The interesting mathematical aspect of the problem is that & is not convex, and usual methods to show existence and uniqueness of the minimum do not apply. By using symmetric decreasing rearrangement inequalities we are able to prove existence and uniqueness (modulo translations) of a minimizing Φ. To prove uniqueness a strict form of the inequality, which we believe is new, is employed.

The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation

Abstract: A detailed analysis is given to the solution of the cubic Schrodinger equation iqt + qxx + 2|q|2q = 0 under the boundary conditions as |x|→∞. The inverse-scattering technique is used, and the asymptotic state is a series of solitons. However, there is no soliton whose amplitude is stationary in time. Each soliton has a definite velocity and “pulsates” in time with a definite period. The interaction of two solitons is considered, and a possible extension to the perturbed periodic wave [q(x + T,t) = q(x,t) as |x|→∞] is discussed.

Contour Enhancement, Short Term Memory, and Constancies in Reverberating Neural Networks

Abstract: This article is the first of a series to globally analyse competitive dynamical systems. The article suggests that competition solves a sensitivity problem that confronts all cellular systems: the noise-saturation dilemma. Low energy input patterns can be registered poorly by cells due to their internal noise. High energy input patterns can be registered poorly by cells because their sensitivity approaches zero when all their sites are turned on. How do cells balance between the two equally deadly, but complementary, extremes of noise and saturation? How do cells achieve a Golden Mean?