6533b7d4fe1ef96bd1261eb8
RESEARCH PRODUCT
Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation
Nikola StoilovKenneth D.t-r MclaughlinChristian Kleinsubject
ComputationFOS: Physical sciences010103 numerical & computational mathematicsFixed point01 natural sciencesRegularization (mathematics)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Davey-Stewartson equationsFOS: MathematicsApplied mathematicsMathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]Mathematics[PHYS]Physics [physics]Nonlinear Sciences - Exactly Solvable and Integrable SystemsScattering010102 general mathematicsStatistical and Nonlinear PhysicsD-bar problemsNumerical Analysis (math.NA)Condensed Matter PhysicsFourier spectral methodGeneralized minimal residual methodIntegral equationAlgebraic equationInverse scattering problemExactly Solvable and Integrable Systems (nlin.SI)Limitdescription
International audience; The inverse scattering approach for the defocusing Davey–Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-12-15 |