TY - JOUR

T1 - Integral representations of solutions of the wave equation based on relativistic wavelets

AU - Perel, Maria

AU - Gorodnitskiy, Evgeny

PY - 2012

Y1 - 2012

N2 - A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincare group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coeffici

AB - A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincare group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coeffici

U2 - 10.1088/1751-8113/45/38/385203

DO - 10.1088/1751-8113/45/38/385203

M3 - Article

VL - 45

SP - 385203_1-14

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 38

ER -