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Reorientational Versus Kerr Dark And Gray Solitary Waves Using Modulation Theory, Prof. Tim Marchant
Reorientational Versus Kerr Dark And Gray Solitary Waves Using Modulation Theory, Prof. Tim Marchant
Tim Marchant
We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrodinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive …
The Analytical Evolution Of Nls Solitons Due To The Numerical Discretization Error, Prof. Tim Marchant
The Analytical Evolution Of Nls Solitons Due To The Numerical Discretization Error, Prof. Tim Marchant
Tim Marchant
Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrodinger equation. Two important implicit numerical schemes for the nonlinear Schrodinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank-Nicolson scheme and a scheme, due to Taha [1], based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t(-1/2), which is characteristic …