Local existence of solutions for the modified Korteweg-de Vries (mKdV) equation in weighted Sobolev spaces
DOI:
https://doi.org/10.46932/sfjdv2n1-034Keywords:
Korteweg-de Vries, weighted Sobolev, deformation of the eyeball, dna breathing, helical spaces curves of LambAbstract
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].
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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
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