Iteration methods for stability spectra of solitary waves

DOI10.1016/j.jcp.2008.03.039zbMath1145.65062OpenAlexW1994505099MaRDI QIDQ933296

Jianke Yang

Publication date: 21 July 2008

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2008.03.039

zbMATH Keywords

convergencesolitary wavesfinite difference methodlinear stabilitynumerical exampleseigenvaluesnonlinear Schrödinger equationnonlinear wave equationRunge-Kutta methodEuler methodspectral methoditeration methodstime evolution equations

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Second-order nonlinear hyperbolic equations (35L70) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (9)

Spatial solitons in PT symmetric potential with competing gain and loss ⋮ Stability of one and two-dimensional spatial solitons in a cubic-quintic-septimal nonlinear Schrödinger equation with fourth-order diffraction and \(\mathcal{PT}\)-symmetric potentials ⋮ Two dimensional gap solitons in self-defocusing media with PT-symmetric superlattice ⋮ Spatial solitons in double-well potentials ⋮ Lanczos-Chebyshev pseudospectral methods for wave-propagation problems ⋮ Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction ⋮ \(\mathcal{PT}\) symmetric nonlinear optical lattice: analytical solutions ⋮ Nonlinear localized modes in \(\mathcal{PT}\)-symmetric optical media with competing gain and loss ⋮ Stability of Gaussian-type soliton in the cubic-quintic nonlinear media with fourth-order diffraction and \(\mathcal{PT}\)-symmetric potentials

Uses Software

• Matlab
• eigs
• ARPACK
• IRAM

Cites Work

• Unnamed Item
• Why Newton's method is hard for travelling waves: small denominators, KAM theory, Arnold's linear Fourier problem, non-uniqueness, constraints and erratic failure
• 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
• Optimizing Schrödinger Functionals Using Sobolev Gradients: Applications to Quantum Mechanics and Nonlinear Optics
• Accelerated Imaginary‐time Evolution Methods for the Computation of Solitary Waves
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Vector Solitons and Their Internal Oscilliations in Birefringent Nonlinear Optical Fibers
• ARPACK Users' Guide
• Spectral Methods in MATLAB
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions

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