Numerical studies on a novel split-step quadratic B-spline finite element method for the coupled Schrödinger-KdV equations

DOI10.1016/j.cnsns.2010.06.003zbMath1221.65253OpenAlexW2064432930MaRDI QIDQ718437

Dongmei Bai, Lu-Ming Zhang

Publication date: 23 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2010.06.003

zbMATH Keywords

initial-boundary value problemfull-discrete schemesplit-step \(B\)-spline finite element methodthe coupled Schrödinger-KdV equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (7)

Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations ⋮ High-order Runge-Kutta structure-preserving methods for the coupled nonlinear Schrödinger-KdV equations ⋮ Time-splitting combined with exponential wave integrator Fourier pseudospectral method for Schrödinger-Boussinesq system ⋮ Petrov-Galerkin method for the coupled Schrödinger-KdV equation ⋮ Efficient schemes for the coupled Schrödinger-KdV equations: decoupled and conserving three invariants ⋮ An extension of the optimal homotopy asymptotic method to coupled Schrödinger-KdV equation ⋮ A simple and robust boundary treatment for the forced Korteweg-de Vries equation

Cites Work

• Unnamed Item
• Unnamed Item
• The finite element method for the coupled Schrödinger-KdV equations
• Numerical solution of complex modified Korteweg-de Vries equation by collocation method
• Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem
• Family of numerical methods based on non-polynomial splines for solution of contact problems
• Solutions of the von Kàrmàn equations via the non-variational Galerkin-B-spline approach
• Galerkin finite element methods for parabolic problems
• B-spline finite elements and their efficiency in solving relativistic mean field equations
• On the solution of the coupled Schrödinger-KdV equation by the decomposition method
• Septic B-spline method of the Korteweg-de Vries-Burgers equation
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• New applications of variational iteration method
• Modified Nodal Cubic Spline Collocation For Poisson's Equation
• Dynamics of coupled solitons
• Finite-dimensional behavior of global attractors for weakly damped and forced kdv equations coupling with nonlinear schrödinger equations
• An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity
• Existence and stability of ground-state solutions of a Schrödinger—KdV system
• A Relaxation Scheme for the Nonlinear Schrödinger Equation

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