Solutions to the Cauchy problem for the equation iuₜ = Δ + (| u |² )u - (ia / 2)u\,(a > 0,x ∈ Rⁿ ,t > 0);\,u(x,0) = u₀ (x) are considered. Conditions on uo and q are given so that solutions do not exist for all $t > 0$
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Masayoshi Tsutsumi (1984) studied this question.
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