It is found (and numerically illustrated) that the closed formula
for travelling waves can be integrated to the incomplete elliptic
integral of the third kind for certain nonlinearities.


MR2457004 Milovic, Daniela; Biswas, Anjan Doubly periodic solution
for nonlinear Schrödinger's equation with higher order polynomial
law nonlinearity. Internat. J. Theoret. Phys. 47 (2008), no. 12,
3335--3340. 81Q05