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Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations

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Publication:1126796
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zbMath0896.35123MaRDI QIDQ1126796

Frank Merle

Publication date: 5 August 1998

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/226175


zbMATH Keywords

nonlinear Schrödinger equationHamiltonian systemsZakharov equationsformation of singularities in time


Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55)


Related Items

Solutions of the Camassa-Holm equation near the soliton ⋮ The Zakharov system in dimension \(d \geq 4\) ⋮ Blow up in finite time and dynamics of blow up solutions for the 𝐿²–critical generalized KdV equation ⋮ Existence of blow-up solutions in the energy space for the critical generalized KdV equation ⋮ Hydrodynamic approach to constructing solutions of the nonlinear Schrödinger equation in the critical case ⋮ Blow-up solutions of inhomogeneous nonlinear Schrödinger equations ⋮ A smoothing property for the \(L^2\)-critical NLS equations and an application to blowup theory ⋮ Instability of the soliton for the focusing, mass-critical generalized KdV equation



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