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Nick P
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Why Does a quadratic phase term in BNLS causes collapse?
the other thing to look for then would be the pseudo conformal invariance of the associated action, corresponding to the so called lens transformation. i don't know much about the BNLS, but some googling yielded this paper which might be of assistance: math.tau.ac.il/~fibich/Manuscripts/BNLS_SIAP10.pdf
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Why Does a quadratic phase term in BNLS causes collapse?
Sulem, C., & Sulem, P. L. (Eds.). (1999). The nonlinear Schrödinger equation: self-focusing and wave collapse (Vol. 139). Springer.
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Why Does a quadratic phase term in BNLS causes collapse?
What about the normal conditions (generally on the sign of the Hamiltonian, plus some constraints on the IC) that one has for the NLSE? This might give some insight. See Ch. 5 of Sulem and Sulem for details.