Merle, Frank Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations. (English) Zbl 0896.35123 Doc. Math., Extra Vol. ICM Berlin 1998, vol. III, 57-66 (1998). Summary: We review qualitative properties of solutions of critical nonlinear Schrödinger equation \[ iu_t= -\Delta u-| u|^{p-1}u, \quad u(0)= u_0, \] and Zakharov equations \[ iu_t= -\Delta u+nu, \quad n_t= -\nabla\cdot v, \quad \frac{1}{c_0^2} v_t= -\nabla(n+| u|^2), \] which develop a singularity in finite time. Cited in 9 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35B40 Asymptotic behavior of solutions to PDEs 35J60 Nonlinear elliptic equations Keywords:Zakharov equations; formation of singularities in time; Hamiltonian systems; nonlinear Schrödinger equation × Cite Format Result Cite Review PDF Full Text: EuDML EMIS