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Odd periodic waves and stability results for the defocusing mass‐critical Korteweg‐de Vries equation
Author(s) -
Natali Fábio,
Amaral Sabrina
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6117
Subject(s) - mathematics , floquet theory , korteweg–de vries equation , eigenvalues and eigenvectors , hessian matrix , mathematical analysis , stability (learning theory) , operator (biology) , monodromy matrix , mathematical physics , nonlinear system , physics , biochemistry , chemistry , repressor , quantum mechanics , machine learning , computer science , transcription factor , gene
In this paper, we present results of existence and stability of odd periodic traveling wave solutions for the defocusing mass‐critical Korteweg‐de Vries equation. The existence of periodic wave trains is obtained by solving a constrained minimization problem. Concerning the stability, we use the Floquet theory to determine the behavior of the first three eigenvalues of the linearized operator around the wave, as well as the positiveness of the associated Hessian matrix.