Rigorous justification of the short-pulse equation
نویسندگان
چکیده
We prove that the short-pulse equation, which is derived from a quasilinear Klein–Gordon equation with formal asymptotic methods, can be rigorously justified. The justification procedure applies to small-norm solutions of the short-pulse equation. Although the small-norm solutions exist for infinite times and include modulated pulses and their elastic interactions, the error bound for arbitrary initial data can only be controlled over finite time intervals.
منابع مشابه
- Short Pulses in Linear and Nonlinear Media
We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium at the left endpoint can be approximated by a linear wave equation which can then be further reduced to the linear short-pulse equation. A rigorous proof is g...
متن کاملThe study of propagation of a femtosecond laser pulse in the breast tissue
In this paper, the evaluation of time profile of a femtosecond pulse laser propagated through biological tissues is studied. The majority of the biological tissues with a high scattering anisotropy must be considered as turbid media, that their optical responses are complicated. To study the propagation of ultra-short pulse in turbid media, the diffuse equation is used. In this study, the analy...
متن کاملTime Frequency Analysis of Higher Harmonic Generation in a Three Color Laser Pulse
high harmonic generation is a useful tool for the generation of short, intense attosecond pulses. In order to simulate high harmonic generation, we performed a numerical solution to the time dependent Schrödinger equation. by considering dipole approximation, we predicted generation of a 53 attosecond pulse. In order to see the time and frequency of emission of attosecond pulse, we exploit...
متن کاملInvestigation of Pressure Pulse Distribution in Porous Media
Diffusivity equation commonly used for pressure distribution prediction in porous media results from substituting equation of state and continuity equation in Navier-Stokes momentum equation. From mathematical point of view this equation format shows infinite propagation speed for pressure pulse through porous media, which is physically impossible. This issue may caused by numerous assumption...
متن کاملFurther studies on relic neutrino asymmetry generation II : a rigorous treatment of repopulation in the adiabatic limit
We derive an approximate relic neutrino asymmetry evolution equation that systematically incorporates repopulation processes from the full quantum kinetic equations (QKEs). It is shown that in the collision dominant epoch, the said equation reduces precisely to the expression obtained previously from the static/adiabatic approximation. The present treatment thus provides a rigorous justificatio...
متن کامل