Results 41 to 50 of about 2,922 (139)

Conformal scattering for a nonlinear wave equation on a curved background

, 2010
The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.
Bachelot A., Bachelot A., Bachelot A., Cagnac F., Choquet-Bruhat Y., Christodoulou D., Chruściel P. T., Corvino J., Friedlander F. G., Geroch R., Hebey E., Häfner D., Häfner D., JÉRÉMIE JOUDIOUX, Penrose R., Penrose R.   +15 more
core   +2 more sources

Second harmonic generation: Goursat problem on the semi-strip and explicit solutions

, 2004
A rigorous and complete solution of the initial-boundary-value (Goursat) problem for second harmonic generation (and its matrix analog) on the semi-strip is given in terms of the Weyl functions.
Ablowitz M J, Akhmanov S A, Alexander Sakhnovich, Bass F G, Cie?li?ski J, Duistermaat J J, Faddeev L D, Gohberg I, Kac M, Kaup D J, Kaup D J, Khusnutdinova K R, Krichever I M, Levitan B M, Liouville J, Marchenko V A, Matveev V B, Miura R, Sakhnovich A L, Sakhnovich A L, Sakhnovich A L, Sakhnovich A L, Sakhnovich L A, Sakhnovich L A, Simon B, Steudel H, Zhiber A V   +26 more
core   +1 more source

Generic solutions for some integrable lattice equations

, 1994
We derive the expressions for $\psi$-functions and generic solutions of lattice principal chiral equations, lattice KP hierarchy and hierarchy including lattice N-wave type equations.
G. Segal, I.M. Krichever, L. V. Bogdanov, M.J. Ablowitz, T. Miwa, V.E. Zakharov   +5 more
core   +1 more source

Generalized solutions to a non-Lipschitz Goursat problem [PDF]

Differential Equations & Applications, 2009
In this paper we investigate solutions to the semi-linear wave equation in canonical form with non Lipschitz non-linearity and distributions or other generalized functions as data. To give a meaning to the Goursat problem with irregular data, we replace it by a biparametric family of problems.
openaire   +2 more sources

Nilpotentization of the kinematics of the n-trailer system at singular points and motion planning through the singular locus

, 2000
We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an
Pasillas-Lepine, William, Respondek, Witold   +1 more
core   +2 more sources

Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem. [PDF]

Ann Henri Poincare, 2023
Finster F, Paganini CF.
europepmc   +1 more source

Complete spelling rules for the Monster tower over three-space

, 2016
The Monster tower, also known as the Semple tower, is a sequence of manifolds with distributions of interest to both differential and algebraic geometers. Each manifold is a projective bundle over the previous.
Castro, Alex L, Howard, Wyatt, Shanbrom, Corey   +2 more
core  

The global Goursat problem on R × S1

Journal of Functional Analysis, 1989
AbstractThe Goursat problem for the nonlinear wave equation (∂τ2 − ∂ϱ2) φ + g(φ) = 0 on R × S1 is treated for Goursat data φ¦c in the Sobolev space H(C) = L2, 1(C), where the lightcone C = {τ = ¦ϱ¦} is identified with S1 by means of the coordinate ϱ ϵ [−π, π]. If g ϵ C1(R), there is a unique local solution given arbitrary Goursat data in H(C).
Baez, John C, Zhou, Zhengfang
openaire   +1 more source

THE GOURSAT PROBLEM FOR HYPERBOLIC LINEAR THIRD ORDER EQUATIONS

Mathematical Modelling and Analysis, 2001
The third order hyperbolic linear differential equation is considered in the non‐cylindrical domain of multidimensional Euclidean space. The equation operator is a composition of a differentiation operator of the first order and second order operator, which is hyperbolic with respect to the prescribed vector field.
openaire   +5 more sources

The characteristic Cauchy problem for Dirac fields on curved backgrounds

, 2009
On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex.
Hafner, Dietrich, Nicolas, Jean-Philippe
core   +1 more source