0000000000384502

AUTHOR

K. Roidot

showing 2 related works from this author

Numerical Study of the semiclassical limit of the Davey-Stewartson II equations

2014

We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…

Critical timeOne-dimensional spaceGeneral Physics and AstronomySemiclassical physicsFOS: Physical sciences01 natural sciences010305 fluids & plasmassymbols.namesakeMathematics - Analysis of PDEsSquare root0103 physical sciencesFOS: Mathematics0101 mathematicsNonlinear Schrödinger equationScalingNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsMathematicsNonlinear Sciences - Exactly Solvable and Integrable SystemsApplied Mathematics010102 general mathematicsMathematical analysisStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Norm (mathematics)symbolsGravitational singularityExactly Solvable and Integrable Systems (nlin.SI)Analysis of PDEs (math.AP)
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Numerical study of the long wavelength limit of the Toda lattice

2014

We present the first detailed numerical study of the Toda equations in $2+1$ dimensions in the limit of long wavelengths, both for the hyperbolic and elliptic case. We first study the formal dispersionless limit of the Toda equations and solve initial value problems for the resulting system up to the point of gradient catastrophe. It is shown that the break-up of the solution in the hyperbolic case is similar to the shock formation in the Hopf equation, a $1+1$ dimensional singularity. In the elliptic case, it is found that the break-up is given by a cusp as for the semiclassical system of the focusing nonlinear Schr\"odinger equation in $1+1$ dimensions. The full Toda system is then studie…

Nonlinear Sciences - Exactly Solvable and Integrable SystemsLong wavelength limitApplied MathematicsFOS: Physical sciencesGeneral Physics and AstronomySemiclassical physicsStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Schrödinger equationNonlinear systemsymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable SystemsSingular solutionsymbolsInitial value problemExactly Solvable and Integrable Systems (nlin.SI)Toda latticeNonlinear Schrödinger equationMathematical PhysicsMathematicsMathematical physicsNonlinearity
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