Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation
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Publication:5231327
DOI10.1137/18M1215050zbMath1419.35178arXiv1809.02725OpenAlexW2962839519WikidataQ127547579 ScholiaQ127547579MaRDI QIDQ5231327
Publication date: 26 August 2019
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.02725
convergence analysisfractional Korteweg-de Vries equationPetviashvili's methodtraveling periodic waves
Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) KdV equations (Korteweg-de Vries equations) (35Q53) Numerical solutions to equations with nonlinear operators (65J15) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)
Related Items (12)
The generalized fractional Benjamin-Bona-Mahony equation: analytical and numerical results ⋮ Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study ⋮ Periodic waves in the fractional modified Korteweg-de Vries equation ⋮ New traveling solutions of the fractional nonlinear KdV and ZKBBM equations with 𝒜ℬℛ fractional operator ⋮ On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation ⋮ Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation ⋮ High order conservative schemes for the generalized Benjamin-Ono equation on the unbounded domain ⋮ Solving nonlinear non-local problems using positive square-root operators ⋮ Green's function for the fractional KdV equation on the periodic domain via Mittag-Leffler function ⋮ On abundant new solutions of two fractional complex models ⋮ Stability of periodic waves for the fractional KdV and NLS equations ⋮ Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation
Uses Software
Cites Work
- Unnamed Item
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- Periodic traveling-wave solutions of nonlinear dispersive evolution equations
- Bilinear transformation method
- Maximum principles for fractional differential equations derived from Mittag-Leffler functions
- Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane
- On well-posedness for some dispersive perturbations of Burgers' equation
- Efficient computation of steady solitary gravity waves
- Perturbation theory for linear operators.
- Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem
- Applied functional analysis. Applications to mathematical physics. Vol. 1
- Fast accurate computation of the fully nonlinear solitary surface gravity waves
- Orbital stability in the cubic defocusing NLS equation. I: Cnoidal periodic waves
- Petviashvili type methods for traveling wave computations. II: Acceleration with vector extrapolation methods
- Algebraic and analytical tools for the study of the period function
- An extended Petviashvili method for the numerical generation of traveling and localized waves
- Counting unstable eigenvalues in Hamiltonian spectral problems via commuting operators
- Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave systems
- 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
- Stability of Small Periodic Waves in Fractional KdV-Type Equations
- Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
- Nonlinear Waves in Integrable and Nonintegrable Systems
- Positivity Properties of the Fourier Transform and the Stability of Periodic Travelling-Wave Solutions
- A class of Hamiltonian systems with increasing periods.
- Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth
- Existence of periodic travelling-wave solutions of nonlinear, dispersive wave equations
- Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations
- Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation
- An efficient method to compute solitary wave solutions of fractional Korteweg–de Vries equations
- Modulational Instability and Variational Structure
- Modulational Instability in the Whitham Equation for Water Waves
- Count of eigenvalues in the generalized eigenvalue problem
- Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation
- Dispersive Perturbations of Burgers and Hyperbolic Equations I: Local Theory
- Model equations for long waves in nonlinear dispersive systems
- Positive solutions for boundary value problem of nonlinear fractional differential equation
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