Search results for "Peregrine solution"

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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Numerical study of the stability of the Peregrine solution

2017

International audience; The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.

PhysicsRogue wavesGeneral Medicine01 natural sciencesStability (probability)010305 fluids & plasmasDeep waterSchrödinger equationsymbols.namesakeNonlinear systemClassical mechanics[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]Peregrine solution0103 physical sciencessymbolsNonlinear Schrödinger equation[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Rogue wave010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsNonlinear Schrödinger equationSchrödinger's cat
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