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

Authors

  • Milton M. Cortez Gutiérrez
  • Hernan O. Cortez Gutiérrez
  • Girady I. Cortez Fuentes Rivera
  • Liv J. Cortez Fuentes Rivera
  • Deolinda E. Fuentes Rivera Vallejo

DOI:

https://doi.org/10.46932/sfjdv2n1-034

Keywords:

Korteweg-de Vries, weighted Sobolev, deformation of the eyeball, dna breathing, helical spaces curves of Lamb

Abstract

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..  Further results can be found in Bona,J.L.-Souganidis,P.E. and Strauss,W.A.  .

Connections with biophysics are illustrated in Cortez, H et al [27]-[29].

Published

2021-05-05

How to Cite

Gutiérrez , M. M. C. ., Gutiérrez, H. O. C. . . . . ., Rivera, G. I. C. F. ., Rivera , L. J. C. F. ., & Vallejo, D. E. F. R. . (2021). Local existence of solutions for the modified Korteweg-de Vries (mKdV) equation in weighted Sobolev spaces. South Florida Journal of Development, 2(1), 458–466. https://doi.org/10.46932/sfjdv2n1-034

Most read articles by the same author(s)