Events Calendar
May 29
14:00 - 15:00
Mathematical Physics & Integrable Systems seminar: Robert Parini (University of York)
SMSAS Mathematical Physics seminars
Sine-Gordon with integrable and near-integrable boundaries


I will discuss the sine-Gordon equation on the half-line with two different boundary conditions.  Firstly, I will present algebro-geometric solutions satisfying the integrable boundary condition u_x = A sin((u-B)/2).  These solutions are periodic or quasi-periodic and can be constructed either by solving a corresponding boundary condition for the Lax eigenfunctions or by the application of a Bäcklund transformation to the known algebro-geometric solutions for sine-Gordon with a Dirichlet boundary.

I will then discuss the collision of solitons with the typically non-integrable Robin boundary, u_x + 2ku=0, parameterised by k. As k varies from 0 to infinity the boundary interpolates between the integrable Neumann and Dirichlet boundaries.  The soliton content of the field after the collision is determined by numerically computing the discrete scattering data associated with the inverse scattering transform.  It is found that, depending on k and the initial soliton velocity, one or more kinks, antikinks or breathers can be produced by the soliton/boundary collision.  In particular, an intricate resonance structure is observed, caused by the production of an intermediate breather whose recollision with the boundary is highly dependent on the breather phase.


Sibson Building (SibSR2)
United Kingdom


Open to All interested persons,

Contact: Dr Pavlos Xenitidis
School of Mathematics, Statistics and Actuarial Science


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Last Updated: 10/01/2012