Solitons, pulse splitting, and AM–FM conversion in cylindrical ducts

Larraza, Andrés; Coleman, William F.

doi:10.1121/1.415949

Cited by 4 publications

(3 citation statements)

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“…For example, essentially the same equations arise in the description of modulations of transverse modes in acoustic 14,15 and model 16 waveguides, as well as surface cross modes in a channel of liquid. [18][19][20][21] To determine the equations that describe the modulations ͑24͒ for the nonanalytic lattice represented by Eqs.…”

Section: Lattices and Nonlinear Schrö Dinger Equationsmentioning

confidence: 90%

Nonanalytic nonlinear oscillations: Christiaan Huygens, quadratic Schrödinger equations, and solitary waves

Denardo

1998

The Journal of the Acoustical Society of America

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An example of an oscillatory system with a time-reversible nonanalytic nonlinearity is shown to be a pendulum with a flexible cord sandwiched between two identical circular disks, in contrast to the analytic case of a pendulum interrupted by a single circular disk. The amplitude-dependent frequencies of both cases are perturbatively calculated, and are compared to numerical simulations over the entire range of amplitudes. The nonanalyticity causes the unusual effect of the frequency to vary linearly with amplitude for small amplitudes, which has also been observed in the resonant frequencies of compressional standing waves in sandstone. A general condition for a nonanalytic nonlinearity to yield this behavior is presented. The amplitude-dependent frequency for the double-interrupted pendulum allows an explanation for Huygens'surprising observation that circular interrupters were as effective as cycloidal interrupters in achieving isochronous motion. A lattice of linearly coupled double-interrupted pendulums is described near the lower and upper cutoff modes by quadratic nonlinear Schrödinger ͑NLS͒ equations, in contrast to cubic NLS equations which arise for analytic pendulum lattices as well as typical acoustic and surface waveguides. Solitary breather and kink solutions to the quadratic NLS equations are presented, and are compared to the known soliton solutions of the corresponding cubic NLS equations. Compressional waves in sandstone are shown to be modeled by the inclusion of a nonanalytic quadratic nonlinearity in the stress-strain relationship. Quadratic NLS breathers are predicted to occur in a waveguide of sandstone, and an analysis indicates that such an observation is feasible.

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Section: Lattices and Nonlinear Schrö Dinger Equationsmentioning

confidence: 90%

Nonanalytic nonlinear oscillations: Christiaan Huygens, quadratic Schrödinger equations, and solitary waves

Denardo

1998

The Journal of the Acoustical Society of America

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“…Azimuthal modes in a nondegenerate ͑e.g., elliptical͒ waveguide have been predicted to support these solitons. 4 Because a compression has higher temperature than a rarefaction, it may be possible to employ acoustic solitons as means to transport localized ''heat patches'' in heat pumps.…”

mentioning

confidence: 99%

“…This mechanism thus allows the possibility of tunable coherent light from a single-frequency coherent source. 4 Another recent application of waveguides is in the determination of stress-strain relations in rocks. Rock is extremely nonlinear, and its static and dynamic behavior exhibits hysteresis and discrete memory.…”

mentioning

confidence: 99%