@article{Arruda2022, 
author = {Lynnyngs K. Arruda},
title = {Multi-shockpeakons for the stochastic Degasperis-Procesi equation},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {6},
pages = {2303-2320},
keywords = {the stochastic Degasperis-Procesi equation, the deterministic Degasperis-Procesi equation, multiplicative noise, Stratonovich stochastic process, multi-peakons, multi-shockpeakons},
url = {https://www.sciopen.com/article/10.3934/era.2022117},
doi = {10.3934/era.2022117},
abstract = {The deterministic Degasperis-Procesi equation admits weak multi-shockpeakon solutions of the form   u(x,t)=∑i=1nmi(t)e−|x−xi(t)|−∑i=1nsi(t)sgn(x−xi(t))e−|x−xi(t)|,where  sgn(x) denotes the signum function with  sgn(0)=0, if and only if the time-dependent parameters  xi(t) (positions),  mi(t) (momenta) and  si(t) (shock strengths) satisfy a system of  3n ordinary differential equations. We prove that a stochastic perturbation of the Degasperis-Procesi equation also has weak multi-shockpeakon solutions if and only if the positions, momenta and shock strengths obey a system of  3n stochastic differential equations.}
}