Sine-Gordon theory in a semi-strip

Abstract

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.

References in corpus (3)

• Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
• Weyl functions, inverse problem and special solutions for the system auxiliary to the nonlinear optics equation
• Quantum complex sine-Gordon model on a half line

Cited by in corpus (5)

• Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation, and Linear Response
• Recovery of Dirac system from the rectangular Weyl matrix function
• On the factorization formula for fundamental solutions in the inverse spectral transform
• Skew-self-adjoint Dirac systems with a rectangular matrix potential: Weyl theory, direct and inverse problems
• Weyl functions and the boundary value problem for a matrix nonlinear Schrödinger equation on a semi-strip