Biomedical subjects

A R Champneys

Publications and source records attributed to A R Champneys.

4 recordsLinked to original sources

PubMed2006

Radiationless traveling waves in saturable nonlinear Schrödinger lattices.

The long-standing problem of moving discrete solitary waves in nonlinear Schrödinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose grand-canonical energy barrier vanishes for isolated coupling strength values. Genuinely localized traveling waves are computed as a function of the system parameters for the first time. The relevant solutions exist only for finite velocities.

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PubMed2005

Accumulation of embedded solitons in systems with quadratic nonlinearity.

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multiwave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero solution has a fourfold zero eigenvalue. In this paper, the existence of such solutions is studied in a three-wave model. An appropriate rescaling casts the system in a normal form, which is universal for models supporting ESs through quadratic nonlinearities. The normal-form system contains a single irreducible parameter epsilon, and is tantamount to the basic model of type-I second-harmonic generation. An analytical approximation of Wentzel-Kramers-Brillouin type yields an asymptotic formula for the distribution of discrete values of epsilon at which the ESs exist. Comparison with numerical results shows that the asymptotic formula yields an exact value of the scaling index, -65, and a fairly good approximation for the numerical factor in front of the scaling term.

Algorithms↗

PubMed2001

Walking cavity solitons.

A family of walking solitons is obtained for the degenerate optical parametric oscillator below threshold. The loss-driven mechanism of velocity selection for these structures is described analytically and numerically. Our approach is based on understanding the role played by the field momentum and generic symmetry properties and, therefore, it can be easily generalized to other dissipative multicomponent models with walk off.

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PubMed2001

Grazing and border-collision in piecewise-smooth systems: a unified analytical framework.

A comprehensive derivation is presented of normal form maps for grazing bifurcations in piecewise smooth models of physical processes. This links grazings with border-collisions in nonsmooth maps. Contrary to previous literature, piecewise linear maps correspond only to nonsmooth discontinuity boundaries. All other maps have either square-root or (3/2)-type singularities.

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