Results 11 to 20 of about 175 (144)

Nonlinear d’Alembert formula for discrete pseudospherical surfaces [PDF]

Journal of Geometry and Physics, 2017
On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature ...
Kobayashi, Shimpei, Shimpei Kobayashi
core   +5 more sources

D'Alembert formula on finite one-dimensional networks

Journal of Mathematical Analysis and Applications, 2003
We find a d'Alembert type formula for the solution of the Cauchy problem for the wave equation on finite weighted networks. We also discuss the periodicity in time of the solution in terms of the spectrum of the discrete graph associated with the network
Fontana, Luigi, Cattaneo, Carla
core   +4 more sources

Cauchy problem for the system of the general hyperbolic differential equations of the forth order with nonmultiple characteristics

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014
We consider the Cauchy problem for the hyperbolic differential equation of the forth order with nonmultiple characteristics. We generalize this problem from the similar Cauchy problem for the hyperbolic differential equation of the third order with ...
Aleksandr A Andreev, Julia O Yakovleva
doaj   +2 more sources

A matrix D'Alembert formula for coupled wave initial value problems

Computers & Mathematics with Applications, 1998
If C is an invertible matrix in Cr × r, the coupled wave equation initial value problem utt = C2uxx, −∞ < x < ∞, t > 0, u(x, 0) = f(x), and ut(x, 0) = g(x) for −∞ < x < ∞ is studied. A matrix D'Alembert formula for the closed form solution of the coupled
Jódar, L., Goberna, D.
core   +3 more sources

Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation

Journal of Applied Mathematics, 2012
Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in
Gusein Sh. Guseinov
doaj   +3 more sources

Structure of Solutions to Linear Evolution Equations: Extensions of d'Alembert's Formula

Journal of Mathematical Analysis and Applications, 1996
The d'Alembert formula expresses the general solution of the factored equation ∏Nj=1(d/dt−Aj)u=0 asu(t)=∑Nj=1exp(tAj)fj. HereA1,…,ANare (linear) commuting semigroup generators, andAi−Ajis injective fori≠j.
Goldstein, Gisèle Ruiz, Goldstein, Jerome A., Obrecht, Enrico   +2 more
core   +2 more sources

The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2013
To every Darboux integrable system there is an associated Lie group G which is a fundamental invariant of the system and which we call the Vessiot group.
Anderson, I.M., Mark E. Fels, Fels, M.E., Ian M. Anderson   +3 more
core   +5 more sources

The Cauchy problem for a general hyperbolic differential equation of the n-th order with the nonmultiple characteristics

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
In the paper the problem of Cauchy is considered for the hyperbolic differential equation of the n-th order with the nonmultiple characteristics. The Cauchy problem is considered for the hyperbolic differential equation of the third order with the ...
Aleksandr A Andreev, Julia O Yakovleva
doaj   +2 more sources

The analogue of D'Alembert formula for hyperbolic differential equation of the third order with nonmultiple characteristics

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012
The Cauchy problem for the third order hyperbolic differential equation with nonmultiple characteristics is considered. The analogue of D'Alembert formula is obtained as a solution that allows describing the propagation of initial displacement, initial ...
J. O. Yakovleva
doaj   +4 more sources

Construction of algebraic-analytic discrete approximations for linear and nonlinear hyperbolic equations in R^{2}. Part I [PDF]

Opuscula Mathematica, 2007
An algebraic-analytic method for constructing discrete approximations of linear hyperbolic equations based on a generalized d'Alembert formula of the Lytvyn and Riemann expressions for Cauchy data is proposed.
Mirosław Luśtyk, Mykola Prytula
doaj   +1 more source