We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that leads to an integrable non-linear partial differential equation. This equation is an analogue of the Kadomtsev–Petviashvili (of type B) equation.

In a hydroelectric power plant or in a pumping station in order to avoid sudden large increase of pressure due to instantaneous valve closure sometimes a surge tank is installed. The height of surge tank is designed by the highest possible water level during the operation. The theoretical treatment of oscillation in a surge tank is difficult because of the non-linearity of friction term in the ...

The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation a linear differential equations with a singular generator matrix. We derive a general method for reducing the dimensionality of the Master equation by one by using the probability normalization constraint, thus obtaining a affine differential equation with a (non-singula...

Ill PREFACE This Memorandum is part of RAND's continuing search for new ways of utilizing the modern digital computer. The authors present a method for numerically Integrating nonlinear partial differential integral equations, which occur In such fields as radiative transfer and mathematical biology. The method Is then specifically applied to solving a basic equation of transport In a spherical...

The complexity of computing the Galois group of a linear differential equation is of general interest. In a recent work, Feng gave the first degree bound on Hrushovski’s algorithm for computing the Galois group of a linear differential equation. This bound is the degree bound of the polynomials used in the first step of the algorithm for finding a proto-Galois group (see Definition 2.8) and is ...

In the following paper we will consider Navier-Stokes problem and it's interpretation by hyperbolic waves, focusing on wave propagation. We will begin with solution for linear waves, then present problem for non-linear waves. Later we will derive for numerical solution using PDE's. Also we will design a Matlab program to solve and simulate wave propagation. Keywords1: Navier-Stokes equations, F...

In this paper, we establish the existence of travelling wave solution to an intrinsically non-linear differential-integral equation formed as a result of mathematical modelling of the evolution of an asexual population in a changing environment. This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows ...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...