Instability of standing waves for non-linear Schrödinger-type equations
From MaRDI portal
Publication:3775891
DOI10.1017/S014338570000938XzbMath0636.35017OpenAlexW1981068154MaRDI QIDQ3775891
Publication date: 1988
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s014338570000938x
standing waveoptical waveguideslinearly unstablenonlinear Schrödinger-type equationsspace of Lagrangian planes
Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) General topics in linear spectral theory for PDEs (35P05) Nonlinear higher-order PDEs (35G20) Partial differential equations of mathematical physics and other areas of application (35Q99)
Related Items (41)
Stability indices for constrained self-adjoint operators ⋮ The Maslov index and spectral counts for linear Hamiltonian systems on \([0, 1\)] ⋮ On classification of intrinsic localized modes for the discrete nonlinear Schrödinger equation ⋮ The Maslov and Morse indices for Schrödinger operators on \([0,1\)] ⋮ Stability analysis for standing pulse solutions to FitzHugh-Nagumo equations ⋮ Generalized Maslov Indices for Non-Hamiltonian Systems ⋮ Discrete peakons ⋮ Hörmander's index and oscillation theory ⋮ Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ Rate-Induced Tipping in Heterogeneous Reaction-Diffusion Systems: An Invariant Manifold Framework and Geographically Shifting Ecosystems ⋮ Linearized instability for nonlinear schrödinger and klein-gordon equations ⋮ Existence and orbital stability/instability of standing waves with prescribed mass for the \(L^2\)-supercritical NLS in bounded domains and exterior domains ⋮ Computing the Maslov index from singularities of a matrix Riccati equation ⋮ The Maslov index and spectral counts for linear Hamiltonian systems on \(\mathbb{R}\) ⋮ Opening the Maslov box for traveling waves in skew-gradient systems: counting eigenvales and proving (in)stability ⋮ Bifurcation to instability through the lens of the Maslov index ⋮ Unstable gap solitons in inhomogeneous nonlinear Schrödinger equations ⋮ Instability indices for matrix polynomials ⋮ A symplectic perspective on constrained eigenvalue problems ⋮ The Maslov and Morse indices for system Schroedinger operators on \mathBB{R} ⋮ An instability criterion for nonlinear standing waves on nonzero backgrounds ⋮ Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves ⋮ On the Maslov index of multi-pulse homoclinic orbits ⋮ On orbital instability of spectrally stable vortices of the NLS in the plane ⋮ Global existence and blow up of solutions for the inhomogeneous nonlinear Schrödinger equation in \(\mathbb R^2\) ⋮ On the spectra of periodic waves for infinite-dimensional Hamiltonian systems ⋮ Heterogeneity-induced effects for pulse dynamics in FitzHugh-Nagumo-type systems ⋮ Domain walls of single-component Bose--Einstein condensates in external potentials ⋮ Computing the Maslov index for large systems ⋮ Computing the Maslov index of solitary waves. II: Phase space with dimension greater than four ⋮ Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space ⋮ Orbital Stability: Analysis Meets Geometry ⋮ Structural stability of non-ground state traveling waves of coupled nonlinear Schrödinger equations ⋮ Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems ⋮ On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential ⋮ The Morse and Maslov indices for multidimensional Schrödinger operators with matrix-valued potentials ⋮ Dynamical and variational properties of the NLS-\( \delta'_s\) equation on the star graph ⋮ The One-Dimensional Case ⋮ Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation ⋮ Stability of fronts in inhomogeneous wave equations ⋮ Existence and stability of solitary waves for the inhomogeneous NLS
Cites Work
This page was built for publication: Instability of standing waves for non-linear Schrödinger-type equations
