A matrix integral solution to [P, Q]=P and matrix laplace transforms

ar X iv : h ep - t h / 96 10 13 7 v 1 1 7 O ct 1 99 6 A Matrix Integral Solution to [ P , Q ] = P and Matrix Laplace Transforms

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P, Q] = P , where P flows according to the KP hierarchy ∂P/∂t n = [(P n/p) + , P ], with p := ord P ≥ 2; (ii) find a matrix integral representation for the associated τ-function. First we construct an infinite dimensional space W = span C ψ 0 (z), ψ 1 (z),. .. of functions of z ∈ C invariant u...

An Integral Operator Solution to the Matrix Toda Equations

In previous work the author found solutions to the Toda equations that were expressed in terms of determinants of integral operators. Here it is observed that a simple variant yields solutions to the matrix Toda equations. As an application another derivation is given of a differential equation of Sato, Miwa and Jimbo for a particular Fredholm determinant. During the last twenty years, beginnin...

A note on the comparison between Laplace and Sumudu transforms

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Integral Transforms with Exponential Kernels and Laplace Transform

Let X ←−fZ −→gY be a correspondence of complex manifolds. We study integral transforms associated to kernels exp(φ), with φ meromor-phic on Z, acting on formal or moderate cohomologies. Our main applicationis the Laplace transform. In this case, X is the projective compactification ofthe vector space V ' Cn, Y is its dual space, Z = X×Y and φ(z, w) = 〈z,w〉.We obt...