Search results for "Split-step method"

showing 4 items of 4 documents

Diffusion stabilizes cavity solitons in bidirectional lasers

2009

We study the influence of field diffusion on the spatial localized structures (cavity solitons) recently predicted in bidirectional lasers. We find twofold positive role of the diffusion: 1) it increases the stability range of the individual (isolated) solitons; 2) it reduces the long-range interaction between the cavity solitons. Latter allows the independent manipulation (writing and erasing) of individual cavity solitons.

Diffusion (acoustics)Field (physics)FOS: Physical sciencesPhysics::OpticsGallium nitridePattern Formation and Solitons (nlin.PS)Ring (chemistry)Molecular physicslaw.inventionchemistry.chemical_compoundlawQuantum mechanicsClockwiseDiffusion (business)Nonlinear Sciences::Pattern Formation and SolitonsPhysicsRange (particle radiation)Weak signalLaserNonlinear Sciences - Pattern Formation and SolitonsAtomic and Molecular Physics and OpticsSplit-step methodNonlinear Sciences::Exactly Solvable and Integrable SystemschemistryGinzburg–Landau theoryAtomic physicsOptics Express
researchProduct

Generalized differential transform method for nonlinear boundary value problem of fractional order

2015

Abstract In this paper the generalized differential transform method is applied to obtain an approximate solution of linear and nonlinear differential equation of fractional order with boundary conditions. Several numerical examples are considered and comparisons with the existing solution techniques are reported. Results show that the method is effective, easier to implement and very accurate when applied for the solution of fractional boundary values problems.

Numerical AnalysisApplied MathematicsMathematical analysisOrder of accuracyFractional derivativeMixed boundary conditionFractional calculusSplit-step methodModeling and SimulationGeneralized differential transformFree boundary problemCauchy boundary conditionBoundary value problemSpectral methodBoundary value problemNonlinear differential equationMathematicsCommunications in Nonlinear Science and Numerical Simulation
researchProduct

Real lattices modelled by the nonlinear Schrödinger equation and its generalizations

2006

We present the analysis of two dimerized lattices : a bi-inductance electrical network with macroscopic wave modes, an antiferromagnetic chain whith microscopic spin waves. Using the multiple scale technique of reductive perturbation we show that the original discrete equations of motion can be reduced to a Nonlinear Schrodinger equation with complex coefficients for the first system and two coupled Nonlinear Schrodinger equations for the second system. The possible solutions of these equations are discussed in relation with our numerical simulations and real experiments.

PhysicsSplit-step methodNonlinear systemsymbols.namesakeTheoretical and experimental justification for the Schrödinger equationClassical mechanicsSpin waveBreatherQuantum mechanicssymbolsKadomtsev–Petviashvili equationNonlinear Schrödinger equationSchrödinger equation
researchProduct

Some efficient algorithms for the solution of a single nonlinear equation

1981

High order methods for the numerical solution of nonlinear scalar equations are proposed which are more efficient than known procedures, and a unified approach to various methods suggested in literature is given.

Split-step methodNonlinear systemComputational Theory and MathematicsEfficient algorithmApplied MathematicsMathematical analysisScalar (mathematics)Order of accuracyHigh orderComputer Science ApplicationsNumerical stabilityLocal convergenceMathematicsInternational Journal of Computer Mathematics
researchProduct