Singular ring solutions of critical and supercritical nonlinear Schrödinger equations

We present new singular solutions of the nonlinear Schrödinger equation (NLS)

     

Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations

In this paper we establish new results about the existence, stability, and instability of periodic travelling wave solutions related to the critical Korteweg-de Vries equation

u_t+5u⁴u_x+u_xxx=0,