An integrable generalization of the sine-Gordon equation on the half-line

作者：Lenells Jonatan^*

来源：IMA Journal of Applied Mathematics, 2011, 76(4): 554-572.

DOI：10.1093/imamat/hxq049

• inverse spectral theory
• Riemann-Hilbert problem
• boundary-value problem

We analyse a generalization of the sine-Gordon equation in laboratory coordinates on the half-line. Using the Fokas transform method for the analysis of initial boundary-value problems for integrable partial differential equations, we show that the solution u(x, t) can be constructed from the initial and boundary values via the solution of a 2 x 2-matrix Riemann-Hilbert problem.

• 出版日期2011-8