Petviashvilli's method for the Dirichlet problem

DOI10.1007/s10915-015-0023-6zbMath1339.65222arXiv1411.4153OpenAlexW2142665949MaRDI QIDQ283312

F. Blanchet-Sadri, M. Dambrine

Publication date: 13 May 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.4153

zbMATH Keywords

algorithmglobal convergencenonlinear wavessolitary wavesnonlinear Schrödinger equationground stateiterative methodssemilinear elliptic equationnumerical experimentartificial boundary conditionexcited statePetviashvilli's method

Mathematics Subject Classification ID

Nonlinear waves in solid mechanics (74J30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Solitary waves in solid mechanics (74J35) Semilinear elliptic equations (35J61)

Related Items (8)

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study ⋮ Numerical computation of solitary wave solutions of the Rosenau equation ⋮ Higher dimensional generalization of the Benjamin‐Ono equation: 2D case ⋮ Interaction with an obstacle in the 2D focusing nonlinear Schrödinger equation ⋮ High order conservative schemes for the generalized Benjamin-Ono equation on the unbounded domain ⋮ Nonlinear Bound States in a Schrödinger--Poisson System with External Potential ⋮ Edge-localized states on quantum graphs in the limit of large mass ⋮ Boussinesq-Peregrine water wave models and their numerical approximation

Uses Software

• FEniCS
• Triangle

Cites Work

• Unnamed Item
• Semilinear elliptic equations for beginners. Existence results via the variational approach
• Automated solution of differential equations by the finite element method. The FEniCS book
• \(L^ p\)-integrability of the second order derivatives of Green potentials in convex domains
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
• A mode elimination technique to improve convergence of iteration methods for finding solitary waves
• Two-pulse solutions in the fifth-order KdV equation: rigorous theory and numerical approximations
• Petviashvili type methods for traveling wave computations. I: Analysis of convergence
• Singular solutions of theL²-supercritical biharmonic nonlinear Schrödinger equation
• Potential Space Estimates for Green Potentials in Convex Domains
• Accelerated Imaginary‐time Evolution Methods for the Computation of Solitary Waves
• Elliptic Partial Differential Equations of Second Order
• Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations
• Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation
• Applications of functional analysis and operator theory
• Universally‐Convergent Squared‐Operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations

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