122,043 research outputs found
Nontrivial solutions of boundary value problems for second order functional differential equations
In this paper we present a theory for the existence of multiple nontrivial
solutions for a class of perturbed Hammerstein integral equations. Our
methodology, rather than to work directly in cones, is to utilize the theory of
fixed point index on affine cones. This approach is fairly general and covers a
class of nonlocal boundary value problems for functional differential
equations. Some examples are given in order to illustrate our theoretical
results.Comment: 19 pages, revised versio
Giant magnons and non-maximal giant gravitons
We produce the open strings on that correspond to
the solutions of integrable boundary sine-Gordon theory by making use of the
-magnon solutions provided in \cite{KPV} together with explicit moduli.
Relating the two boundary parameters in a special way we describe the
scattering of giant magnons with non-maximal giant gravitons and
calculate the leading contribution to the associated magnon scattering phase.Comment: 34 pages, 8 figure
Asymptotic methods for delay equations.
Asymptotic methods for singularly perturbed delay differential equations are in many ways more challenging to implement than for ordinary differential equations. In this paper, four examples of delayed systems which occur in practical models are considered: the delayed recruitment equation, relaxation oscillations in stem cell control, the delayed logistic equation, and density wave oscillations in boilers, the last of these being a problem of concern in engineering two-phase flows. The ways in which asymptotic methods can be used vary from the straightforward to the perverse, and illustrate the general technical difficulties that delay equations provide for the central technique of the applied mathematician. © Springer 2006
The boundary sine-Gordon theory: classical and semi-classical analysis
We consider the sine-Gordon model on a half-line, with an additional
potential term of the form at the
boundary. We compute the classical time delay for general values of ,
and using -function methods and show that in the
classical limit, the method of images still works, despite the non-linearity of
the problem. We also perform a semi-classical analysis, and find agreement with
the exact quantum S-matrix conjectured by Ghoshal and Zamolodchikov.Comment: 19 pages, 5 figures. Preprint USC-94-013. (Numerical mistake
corrected.
Restricting affine Toda theory to the half-line
We restrict affine Toda field theory to the half-line by imposing certain
boundary conditions at . The resulting theory possesses the same spectrum
of solitons and breathers as affine Toda theory on the whole line. The
classical solutions describing the reflection of these particles off the
boundary are obtained from those on the whole line by a kind of method of
mirror images. Depending on the boundary condition chosen, the mirror must be
placed either at, in front, or behind the boundary. We observe that incoming
solitons are converted into outgoing antisolitons during reflection. Neumann
boundary conditions allow additional solutions which are interpreted as
boundary excitations (boundary breathers). For and Toda
theories, on which we concentrate mostly, the boundary conditions which we
study are among the integrable boundary conditions classified by Corrigan
et.al. As applications of our work we study the vacuum solutions of real
coupling Toda theory on the half-line and we perform semiclassical calculations
which support recent conjectures for the soliton reflection
matrices by Gandenberger.Comment: 39 pages, 4 ps figure
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