Periodic Waves of the Modified KdV Equation as Minimizers of a New Variational Problem

Periodic waves of the modified Korteweg-de Vries (mKdV) equation are identified in context a new variational problem with two constraints. The advantage this is that its nondegenerate local minimizers stable time evolution mKdV equation, whereas saddle points unstable. We explore analytical representation periodic given by Jacobi elliptic functions and compute numerically critical constrained problem. A broken pitchfork bifurcation three smooth solution families found. Two represent (stable) one family represents (unstable) points.