Odd periodic waves and stability results for the defocusing mass-critical Korteweg-de Vries equation

摘要

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.