301 research outputs found
Complex sine-Gordon-2: a new algorithm for multivortex solutions on the plane
We present a new vorticity-raising transformation for the second integrable
complexification of the sine-Gordon equation on the plane. The new
transformation is a product of four Schlesinger maps of the Painlev\'{e}-V to
itself, and allows a more efficient construction of the -vortex solution
than the previously reported transformation comprising a product of maps.Comment: Part of a talk given at a conference on "Nonlinear Physics. Theory
and Experiment", Gallipoli (Lecce), June-July 2004. To appear in a topical
issue of "Theoretical and Mathematical Physics". 7 pages, 1 figur
Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation
We construct exact localised solutions of the PT-symmetric Gross-Pitaevskii
equation with an attractive cubic nonlinearity. The trapping potential has the
form of two -function wells, where one well loses particles while the
other one is fed with atoms at an equal rate. The parameters of the constructed
solutions are expressible in terms of the roots of a system of two
transcendental algebraic equations. We also furnish a simple analytical
treatment of the linear Schr\"odinger equation with the PT-symmetric
double- potential.Comment: To appear in Proceedings of the 15 Conference on Pseudo-Hermitian
Hamiltonians in Quantum Physics, May 18-23 2015, Palermo, Italy (Springer
Proceedings in Physics, 2016
Resonantly driven wobbling kinks
The amplitude of oscillations of the freely wobbling kink in the
theory decays due to the emission of second-harmonic radiation. We study the
compensation of these radiation losses (as well as additional dissipative
losses) by the resonant driving of the kink. We consider both direct and
parametric driving at a range of resonance frequencies. In each case, we derive
the amplitude equations which describe the evolution of the amplitude of the
wobbling and the kink's velocity. These equations predict multistability and
hysteretic transitions in the wobbling amplitude for each driving frequency --
the conclusion verified by numerical simulations of the full partial
differential equation. We show that the strongest parametric resonance occurs
when the driving frequency equals the natural wobbling frequency and not double
that value. For direct driving, the strongest resonance is at half the natural
frequency, but there is also a weaker resonance when the driving frequency
equals the natural wobbling frequency itself. We show that this resonance is
accompanied by translational motion of the kink.Comment: 19 pages in a double-column format; 8 figure
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