Modulation stability analysis of exact multidimensional solutions to the generalized nonlinear Schrödinger equation and the Gross-Pitaevskii equation using a variational approach

We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.