Iryna Karpenko

The sine-Gordon equation in light-cone coordinates on the half-lines revisited: a Riemann–Hilbert approach

Abstract In this work, we study the initial-boundary value (IBV) problems for the sine-Gordon (sG) equation in the light-cone coordinates $$u_{xt}=\sin u$$ u xt = sin u in the quarter-planes $$x> 0, t > 0$$ x > 0 , t > 0 and $$x < 0, t > 0$$ x < 0 , t > 0 , assuming a suitable de...