Abstract
The sine-Gordon equation is one of the three classical
nonlinear partial differential equations possessing soliton solutions
in the case of one spatial dimension. Extending the sine-Gordon equation to
two spatial dimensions is relevant for applications to the dynamics of
large area Josephson junctions. In particular we have investigated
Josephson waveguides consisting of two rectangular large area regions
joined by a bent section of
constant curvature. Transverse homogeneous
and inhomogeneous Neumann boundary conditions are used.
Numerical and approximate analytical tools have been used to investigate
how kink shaped solitons of the sine-Gordon equation propagate through
the bent section. We have found that the region with finite curvature
acts as a potential barrier whose height and width depends on
the radius of curvature of the waveguide. The kink transmission,
reflection and trapping is investigated. The kink may be captured when a
driving force, provided by a magnetic field, is applied to the kink.
The approximate analytical tools are based on a variational approach
of a Lagrangian. The variation is done with respect to collective
coordinates, or slowly varying coefficients, in the 1D soliton solution.
Original language | English |
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Publication date | 2004 |
Publication status | Published - 2004 |
Event | SIAM Nonlinear Waves and Coherent Structures - Orlando, United States Duration: 2 Oct 2004 → 5 Oct 2004 |
Conference
Conference | SIAM Nonlinear Waves and Coherent Structures |
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Country/Territory | United States |
City | Orlando |
Period | 02/10/2004 → 05/10/2004 |