Numerical methods and simulations for the dynamics of one-dimensional Zakharov-Rubenchik equations

DOI10.1007/S10915-013-9768-YzbMath1306.65248OpenAlexW2002567768MaRDI QIDQ474914

Ziyi Li, Xiaofei Zhao

Publication date: 25 November 2014

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

Full work available at URL: https://doi.org/10.1007/s10915-013-9768-y

zbMATH Keywords

stabilityfinite difference methodspectral methodsoliton solutiondiscrete conservation lawtime splittingfinite difference time domain methodZarkharov-Rubenchik equations

Mathematics Subject Classification ID

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) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (6)

Conservative compact difference scheme for the Zakharov–Rubenchik equations ⋮ On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system ⋮ A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov-Rubenchik equations ⋮ Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equations ⋮ Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov-Rubenchik equations ⋮ Two numerical methods for the Zakharov-Rubenchik equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adiabatic limit of the Zakharov-Rubenchik equation
• Well posedness for the 1D Zakharov-Rubenchik system
• Numerical solution of the Zakharov equations
• Benney equations and quasiclassical approximation in the method of the inverse problem
• Existence and smoothing effect of solutions for the Zakharov equations
• On the Cauchy problem for the Zakharov system
• Numerical methods for the generalized Zakharov system.
• Stability of the solitons for the one-dimensional Zakharov-Rubenchik equation
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Conformal maps and reductions of the Benney equations
• Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
• Well-posedness for the Benney-Roskes/Zakharov-Rubenchik system
• Spectral Methods
• A General Theory for Interactions Between Short and Long Waves
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
• On the Construction and Comparison of Difference Schemes

This page was built for publication: Numerical methods and simulations for the dynamics of one-dimensional Zakharov-Rubenchik equations