Local existence of solutions for the modified Korteweg-de Vries (mKdV) equation in weighted Sobolev spaces

Milton M. Cortez Gutiérrez, Hernan O. Cortez Gutiérrez, Girady I. Cortez Fuentes Rivera, Liv J. Cortez Fuentes Rivera, Deolinda E. Fuentes Rivera Vallejo
2021 South Florida Journal of Development  
Our goal in this paper is to give a proof of local existence of solutions for the modified Korteweg-de-Vries (mKdV) in a weighted Sobolev space with initial data. A parabolic regularization is suggested, discussed and implemented for the approximation of solutions for the mKdV equation with an appropriate class of nonlineariy. The study for the mKdV equation and computations of blow-up without weighted was treated by Bona,J.L and Dougalis,V.A.. [4] Further results can be found in
more » ... nidis,P.E. and Strauss,W.A.[6] . Connections with biophysics are illustrated in Cortez, H et al [27]-[29].
doi:10.46932/sfjdv2n1-034 fatcat:gb6koh434ng5nmzqcnkwq46poi