Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations (Q1126796)
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scientific article; zbMATH DE number 1184346
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations |
scientific article; zbMATH DE number 1184346 |
Statements
Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations (English)
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5 August 1998
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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.
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Zakharov equations
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formation of singularities in time
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Hamiltonian systems
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nonlinear Schrödinger equation
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