Search results for "nonlinear Schroedinger equation"

showing 3 items of 3 documents

Chaos and nonlinearities in high harmonic generation

2016

Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic…

Physicseducation.field_of_studynonlinear Schroedinger equationPhysics and Astronomy (miscellaneous)PopulationLinearity01 natural sciencesharmonic generation; nonlinear Schroedinger equation; Instrumentation; Physics and Astronomy (miscellaneous)harmonic generation010309 opticsNonlinear systemsymbols.namesakeQuantum mechanics0103 physical sciencesQuantum systemsymbolsInitial value problemHigh harmonic generation010306 general physicseducationHamiltonian (quantum mechanics)Nonlinear Schrödinger equationInstrumentation
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Thermal solitons in nanotubes

2022

Starting from a recent proposal of a nonlinear Maxwell-Cattaneo equation for the heat transport with relaxational effects at nanoscale, in a special case of thermal-wave propagation we derive a nonlinear Schrodinger equation for the amplitudes of the heatflux perturbation. The complete integrability of the obtained equation is investigated in order to prove the existence of infinite conservation laws, as well as the existence of infinite exact solutions. In this regards, we have considered the simplest nontrivial solutions, namely, the bright and dark (thermal) solitons, which may be interesting for energy transport and for information transmission in phononic circuits. (c) 2022 Elsevier B.…

Complete integrabilityComputational MathematicsThermal solitonsApplied MathematicsModeling and SimulationComplete integrability; Extended Non-Equilibrium Thermodynamics; Maxwell–Cattaneo law; Nonlinear Schrödinger equation; Thermal solitonsNonlinear Schrödinger equationGeneral Physics and AstronomyNonlinear Schroedinger equation Thermal solitons Maxwell-Cattaneo law Extended Non-Equilibrium Thermodynamics Complete integrabilityMaxwell–Cattaneo lawSettore MAT/07 - Fisica MatematicaExtended Non-Equilibrium Thermodynamics
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Soliton solutions for an higher order nonlinear Schroedinger equation in optical fiber

2008

The new improvements to increase the bit rate in optical fiber require the propagation of pulse whose temporal width is always lesser. This causes the presence of further terms, linear and nonlinear, in the evolution equation of the pulse. The analysis on the complete integrability of the evolution equation, in a fiber optics with local properties and achieved in a previous paper, is improved dealing with the normal dispersion case, which allows the dark soliton propagation. In the last section special efforts are made to propose some interesting soliton solutions both bright and dark.

fiber opticSolitonIntegrabilitypartial nonlinear Schroedinger equation.
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