Exact solutions of semiclassical non-characteristic Cauchy problems for the sine-Gordon equation

In the appendices, we give a self-contained account of the Cauchy problem from the perspectives of both inverse scattering and classical analysis (Picard iteration). Specifically, Appendix A contains a complete formulation of the inverse-scattering method for generic L1-Sobolev initial data, and Appendix B establishes the well-posedness for Lp-Sobolev initial data (which in particular completely justifies the inverse-scattering analysis in Appendix A).