On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations

Transversal spectral instability of periodic traveling waves for the generalized Zakharov-Kuznetsov equation

“…In this case, we also have a threshold value c # such that for c P p0, c # s the periodic sign-changing wave ϕ is transversally unstable since pL ´11, 1q L 2 per ď 0. The value of c # can be explicitly computed as c # « 43.665 L 2 0 (see [8] for further details).…”