This thesis investigates the integrability of the sine-Gordon system of nonlinear partial differential equations when the dependent variables are subject to some very particular boundary conditions. In chapter 1 the sine-Gordon system is introduced and, with N ϵ Z, P, Q ϵ R, the sets of initial-boundary value problems A(_N) and B(_P,Q) are defined. In the set A(_N) at the spatial variable x is unbounded and the boundary conditions are fixed by initially choosing the topological charge N. This set of problems is the one usually associated with the sine-Gordon system. In the set B(_P,Q) the spatial coordinate is constrained to the semi-line (-oo,0) and there exists two boundary parameters P,Q ϵ R to be chosen a priori. It is the study of this second set of initial-boundary value problems for arbitrary P, Q which forms all the original work of this dissertation. The study presented here is primarily concerned with the development of three separate inverse scattering methods for solving these sets of initial-boundary value problems. The first of these is developed in chapter 3 and is applicable to a subset of the problems in A(_N). The method is the one usually associated with the sine-Gordon system and studies the asymptotics of the initial data as x → ±oo. It is included in this thesis for completeness and as background for the original material which follows. Next, in chapters 4 and 5, the inverse scattering methods appropriate to initial-boundary value problems in subsets of B(_P,O) and B(_P,Q#O) are constructed. In these cases it is important to realise that it is only possible to study the asymptotics of the initial data as x → -oo. Once these three methods have been formulated they are used to find soliton solutions and infinite sets of integrals of motion for these boundary value problems. When a boundary is present at x = 0 the interaction of the solitons with this boundary is studied. These topics are addressed in chapter 6. Finally in chapter 7 the question of the integrability of both sets of problems is addressed. By interpreting the various inverse scattering methods in terms of canonical coordinate transformations of phase space it is seen that the existence of such methods can be viewed as a constructive proof of the integrability of these boundary value problems.

iv, 124 leaves ; 31 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1977

x, 97 leaves : ill., reprint / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1972

Thesis (Ph. D.)--Oregon State University, 1989. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Pure Mathematics, 1977.

Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1972.

Thesis (M.S. in Electrical and Computer Engineering)--Naval Postgraduate School, December 1990. / Thesis Advisor(s): Atwater, H.A. Second Reader: Lee, H.M. "December 1990." Description based on title screen as viewed on March 30, 2010. DTIC Identifier(s): Circuits, Computerized Simulation, Discontinuities, FORTRAN, SCPL(Shielded Coplanar Line), Theses, Computations, Boundary Value Problems. Author(s) subject terms: A discontinuity study in shielded coplanar line. Includes bibliographical references (p. 57). Also available in print.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1954. / Typescript with manuscript equations. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf [38]).

Thesis (Ph. D.)--West Virginia University, 2000. / Title from document title page. Document formatted into pages; contains v, 74 p. Includes abstract. Includes bibliographical references (p. 71-74).

Issued also as thesis, Bonn. / Added t.p. with thesis statement. Includes bibliographical references (p. 60-61).