1,721,402 research outputs found
Resonance Thirring solitons in type II second-harmonic generation
No full textIt is shown that second-harmonic generation in a grating allows one to cancel the group-velocity difference between two polarization components at fundamental by means of nonlinearly induced phase shifts. This occurs when a new type of cascading soliton propagates on resonance
Dispersive shock waves: from predictions to experiments
No full textReview Lecture on Dispersive Shock Wave
Recurrent nonlinear modulational instability in the beta-FPUT chain
No full textWe address the fully nonlinear stage of seeded modulational instability in the Fermi-Pasta–Ulam-Tsingou chain with quartic interaction potential (??-FPUT) subject to periodic boundary conditions. In particular, we investigate quantitatively the validity of the continuous approximation that describes the evolution of a narrow band of normal modes in terms of the ubiquitous nonlinear Schrödinger equation (NLSE) or its generalizations. By injecting three normal modes comprising a pair of unstable sidebands, we find that the FPUT chain exhibits, for weak enough nonlinear interaction, recurrent evolutions (though of different nature compared with the original work by FPUT). Such recurrences generally preserve the homoclinic structure of nonlinear modulational instability ruled by the NLSE, with generated higher order-modes being essentially enslaved to the unstable pair. Under some circumstance, we find that pseudo-random separatrix crossing events may occur even for a very weak interaction strength.
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Envelope localized waves of the conical type in linear normally dispersive media
No full textNondiffractive and nondispersive localized waves with narrow bandwidth are investigated theoretically as solutions of the linear scalar wave equation for normally dispersive media. By employing a Fourier approach, we study how the features of the linear dispersion relationship, i.e., the transverse wave number as a function of frequency, change as a function of the parameters of the wave and the medium (dispersion). We classify the localized waves accordingly and give their explicit expressions in those special cases which allow
us to solve the Fourier-Bessel integral that yields the general representation of such waves
Nonlinear modulational instability: is it really a Fermi-Pasta-Ulam-Tsingou phenomenon?
No full textThe nonlinear Schrödinger equation models mixing phenomena such as modulational instability in fibers. I ts r egular b ehavior w as a ssociated t o Fermi-Pasta-Ulam-Tsingou recurrence. We rigorously compare their behaviors and clarify this analogy, set-tling a long-lasting debated problem
Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation
No full textWe study the wave breaking mechanism for the weakly dispersive defocusing nonlinear Schrödinger equation with a constant phase dark initial datum that contains a vacuum point at the origin. We prove by means of the exact solution to the initial value problem that, in the dispersionless limit, the vacuum point is preserved by the dynamics until breaking occurs at a finite critical time. In particular, both Riemann invariants experience a simultaneous breaking at the origin. Although the initial vacuum point is no longer preserved in the presence of a finite dispersion, the critical behavior manifests itself through an abrupt transition occurring around the breaking time
Temporal solitons
No full textOptical temporal solitons are non-spreading wavepackets such that dispersive effects are counterbalanced by nonlinear effects. The underlying physical ideas together with the settings where such solitons can be observed are reviewed
Spatial solitons
No full textSpatial solitons are optical beams that do not spread thanks to the mutual compensation of diffraction and nonlinear response of dielectrics. The book reviews the state of the art of the research in this field, both experimentally and theoretically, with contributions from worldwide leading groups. Basic as well as more advanced aspects are covered
Dispersive wave-breaking in coherently driven passive cavities
No full textWe show that the intracavity field evolving in an externally driven passive Kerr resonator subject to weak normal dispersion undergoes wave-breaking, thus forming dispersive shock waves. At variance with the cavity-less propagation, such dispersive wave-breaking turns out to be strongly favored by cavity bistability and coexisting modulational instability
Two-dimensional envelope localized waves in the anomalous dispersion regime
No full textNarrowband localized wave packets that are nondispersing and nondiffracting in one transverse dimension
are characterized in anomalously dispersive media by means of a Fourier approach. Depending on the group
velocity, waves with a dispersion relationship characterized by real wavenumbers can be O or X waves,
while we also find waves with evanescent wavenumbers
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