Justification of modulation equations for hyperbolic systems via normal forms
From MaRDI portal
Publication:1378420
DOI10.1007/s000300050034zbMath0890.35082OpenAlexW2084440218MaRDI QIDQ1378420
Publication date: 29 June 1998
Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s000300050034
First-order nonlinear hyperbolic equations (35L60) NLS equations (nonlinear Schrödinger equations) (35Q55) Normal forms for dynamical systems (37G05)
Related Items
Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth ⋮ Interchanging space and time in nonlinear optics modeling and dispersion management models ⋮ Justification of the 2D NLS equation for a fourth order nonlinear wave equation - quadratic resonances do not matter much in case of analytic initial conditions ⋮ The Validity of Whitham's Approximation for a Klein--Gordon--Boussinesq Model ⋮ Validity of the resonant four-wave interaction system in a model for surface water waves on an infinite deep sea ⋮ Justification of the nonlinear Schrödinger approximation for a quasilinear Klein-Gordon equation ⋮ Validity of amplitude equations for nonlocal nonlinearities ⋮ Rotating spirals in oscillatory media with nonlocal interactions and their normal form ⋮ A robust way to justify the derivative NLS approximation ⋮ Nonlinear Dynamics of a System of Particle-Like Wavepackets ⋮ Validity of the nonlinear Schrödinger approximation for the two-dimensional water wave problem with and without surface tension in the arc length formulation ⋮ Wavepacket preservation under nonlinear evolution ⋮ A Model for the Periodic Water Wave Problem and Its Long Wave Amplitude Equations ⋮ Interaction of modulated pulses in nonlinear oscillator chains ⋮ The Zakharov limit of Klein–Gordon–Zakharov like systems in case of analytic solutions ⋮ Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales ⋮ Modified energy functionals and the NLS approximation ⋮ Justification of the NLS approximation for the KdV equation using the Miura transformation ⋮ Justification of the NLS approximation for a quasilinear water wave model ⋮ Bounds for the nonlinear Schrödinger approximation of the Fermi–Pasta–Ulam system ⋮ NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms ⋮ Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media ⋮ Validity of Whitham's equations for the modulation of periodic traveling waves in the NLS equation ⋮ Justification of the NLS approximation for the Euler-Poisson equation ⋮ Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances ⋮ LINEAR SUPERPOSITION IN NONLINEAR WAVE DYNAMICS ⋮ Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity ⋮ Modulating pulse solutions for quasilinear wave equations ⋮ Deriving amplitude equations via evolutionary \(\Gamma\)-convergence