Focusing of spherical nonlinear pulses in R1+3. II. Nonlinear caustic.

Carles, Rémi, and Rauch, Jeffrey. "Focusing of spherical nonlinear pulses in R1+3. II. Nonlinear caustic.." Revista Matemática Iberoamericana 20.3 (2004): 815-864. <http://eudml.org/doc/39728>.

@article{Carles2004,
abstract = {We study spherical pulse like families of solutions to semilinear wave equattions in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the L∞ norm.},
author = {Carles, Rémi, Rauch, Jeffrey},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones diferenciales hiperbólicas; Ecuación de onda; Ecuaciones en derivadas parciales no lineales; Optica geométrica; Impulsos electromagnéticos; Cáustica; Comportamiento asintótico; high frequency asymptotics; semilinear wave equations; scattering operator},
language = {eng},
number = {3},
pages = {815-864},
title = {Focusing of spherical nonlinear pulses in R1+3. II. Nonlinear caustic.},
url = {http://eudml.org/doc/39728},
volume = {20},
year = {2004},
}

TY - JOUR
AU - Carles, Rémi
AU - Rauch, Jeffrey
TI - Focusing of spherical nonlinear pulses in R1+3. II. Nonlinear caustic.
JO - Revista Matemática Iberoamericana
PY - 2004
VL - 20
IS - 3
SP - 815
EP - 864
AB - We study spherical pulse like families of solutions to semilinear wave equattions in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the L∞ norm.
LA - eng
KW - Ecuaciones diferenciales hiperbólicas; Ecuación de onda; Ecuaciones en derivadas parciales no lineales; Optica geométrica; Impulsos electromagnéticos; Cáustica; Comportamiento asintótico; high frequency asymptotics; semilinear wave equations; scattering operator
UR - http://eudml.org/doc/39728
ER -