6533b873fe1ef96bd12d5993
RESEARCH PRODUCT
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
Miguel ÁNgel García-marchMario ZacarésAlbert FerrandoJavier VijandeLincoln D. Carrsubject
Angular momentumRotational symmetryFOS: Physical sciencesMultidimensional discrete solitonsPattern Formation and Solitons (nlin.PS)01 natural sciences010305 fluids & plasmasSchrödinger equationsymbols.namesake0103 physical sciences010306 general physicsNonlinear Schrodinger equationNonlinear Sciences::Pattern Formation and SolitonsNonlinear Schrödinger equationMathematicsAngular pseudomomentumMathematical analysisFísicaStatistical and Nonlinear PhysicsCondensed Matter PhysicsNonlinear Sciences - Pattern Formation and SolitonsMathematical theoryCondensed Matter - Other Condensed MatterNonlinear systemClassical mechanicsIrreducible representationsymbolsDiscrete symmetry mediaSolitonMATEMATICA APLICADAOther Condensed Matter (cond-mat.other)description
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we explore the possibilities of the generalization of the previous framework to the quantum limit.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-01-01 |