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- W2011479332 abstract "Collapsing solutions in the Cauchy problem of the nonlinear Schrödinger equation i ∂tψ + ∇2ψ +‖ ψ‖pψ = 0 (x∈ℛd) are considered in the so-called critical case pd=4, where d is the spatial dimension. A stability theorem for radial collapse is presented which proves that the formation of the singularity remains ‘‘close’’ to the self-similar collapsing solution with a spatial profile given by the ground state solitary wave, provided the energy H{ψ}<0. An analogous result is given for the scalar Zakharov equations and a generalized Korteweg–de Vries equation ∂tu + (p + 1)up ∂xu + ∇2 ∂xu = 0." @default.
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- W2011479332 date "1992-03-01" @default.
- W2011479332 modified "2023-09-26" @default.
- W2011479332 title "On the stability of collapse in the critical case" @default.
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- W2011479332 doi "https://doi.org/10.1063/1.529749" @default.
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