Sine-Gordon theory in a semi-strip

Initial-boundary value problems for complex sine-Gordon and sine-Gordon equations in a semi–strip are treated. The evolution of the Weyl function and a uniqueness result are obtained for complex sine-Gordon equation. The evolution of the Weyl function as well as an existence result and a procedure to recover solution are given for sine-Gordon equation. It is shown that for a wide class of examples the solutions of the sine-Gordon equation are unbounded in the quarter-plane.