Search results for "dinger equations"

showing 2 items of 2 documents

Numerical study of the transverse stability of the Peregrine solution

2020

We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time integration, based on a splitting scheme and an implicit Runge--Kutta method for the linear part, is presented. Secondly, the 1D code is combined with a Fourier spectral method in the transverse variable both for elliptic and hyperbolic NLS equations. As an example we study the transverse stability of the Peregrine solution, an exact solution to the one dimensional nonlinear Schr\"odinger (NLS) equation and thus a $y$-independent solution to the 2D NLS. It is shown that the Peregrine solution is unstable against all…

Mathematics::Analysis of PDEsFOS: Physical sciences010103 numerical & computational mathematics01 natural sciencesStability (probability)spectral approachdispersive blow-upperfectly matched layersymbols.namesakeMathematics - Analysis of PDEsnonlinear Schrodinger equations0103 physical sciencesFOS: MathematicsMathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsReal lineVariable (mathematics)Physicsschrodinger-equationsNonlinear Sciences - Exactly Solvable and Integrable SystemsApplied MathematicsMathematical analysisNumerical Analysis (math.NA)Nonlinear systemTransverse planeExact solutions in general relativityFourier transformPeregrine solutionsymbolsExactly Solvable and Integrable Systems (nlin.SI)Spectral methodAnalysis of PDEs (math.AP)
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On a nonlinear Schrödinger equation for nucleons in one space dimension

2021

We study a 1D nonlinear Schrödinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied numerically via the time evolution of perturbed ground states. In the time evolution of general localized initial data, they are shown to appear in the long time behaviour of certain cases.

numerical studySpace dimensionNonlinear Schrö010103 numerical & computational mathematicsNonlinear Schrödinger equations01 natural sciencesStability (probability)symbols.namesakeMathematics - Analysis of PDEs[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Mathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]dinger equationsNonlinear Schrödinger equationMathematicsMSC 35Q55 35C08 65M70Numerical AnalysisApplied Mathematics010102 general mathematicsTime evolutionground statesComputational MathematicsClassical mechanicsModeling and SimulationAtomic nucleussymbolsParticleNucleonAnalysis[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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