Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 10 of 10 for “"Lax pair"”.
-
Mathematical Aspects of Field Theory: Nahm's Equations and Jacobi Forms
… equations, which is an integrable system with a Lax pair. We consider boundary conditions on Nahm's equations that correspond to the Dirac multimonopole in Yang-Mills theory. The algebro-geometric integration method is to construct solutions via a linear flow in the Jacobian of the spectral curve …
-
Maxwell-Bloch and nonlinear Schrodinger systems with nonzero background
… structure, and with the existence of a Lax pair. As a result, various analytical methods can be applied to study their solu-tions. In particular, a nonlinear analog of the Fourier transform—the inverse scattering transform (IST)—is a powerful technique that can solve the initial value …
-
Integrable Evolution Partial Differential Equations: Multidimensions and Dirichlet-to-Neumann Maps
… of a set of linear equations, the so-called Lax pair, and can be solved via a method related to the Inverse Scattering Transform. Although integrable systems are quite rare, they play an extremely important role in physical applications, including the theory of water waves and optics. The …
-
Anti-self-dual fields and manifolds
… Using twistorial methods we construct a Lax Pair for Przanowski’s equation, confirming its integrability. The Lee form of a compatible local complex structure gives rise to a conformally invariant differential operator, special cases of the associated generalised Laplace operator are the …
-
TWO RESULTS ON THE GLOBAL DYNAMICS OF PDES ON THE CIRCLE.
… 2 we present preliminary results about the Lax-pair structure of the PDE and the associated Birkhoff coordinates, which are the main properties that we need to introduce in Chapter 3 a Tao-type Gauge transformation G, following the classical strategy developed to prove a smoothing result for …
-
Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field
… completely integrable and can be generated by a Lax pair. The isotropic system is reduced using the Casimirs, via the Euler angles, to a four-dimensional canonical system with a first integral provided the magnetic field is not aligned with the force within the rod at any point as the system …
-
On the discrete nonlinear Schrödinger equation with PT-Symmetry
… (Jost solutions) of the associated Lax pair, the scattering data and the fundamental analytic solutions. In addition, we study the spectral properties of the associated discrete Lax operator. Based on the formulated Riemann-Hilbert problem, we derive the one- and two-soliton …
-
Random tilings : gap probabilities, local and global asymptotics
… [75] of type A(1)/2. We also calculate its Lax pair. Following [7], we introduce the notion of the [tau]-function of a q-connection and its isomonodromy transformations. We show that the gap probability function of the q-Hahn ensemble can be viewed as the [tau]-function for an associated …
-
Soliton solutions of noncommutative integrable systems
… dependent variables in either the hierarchy or Lax pair generating the equation. Both Chapters 1 and 2 are entirely made up of background material and contain no new material. Furthermore, these chapters are concerned with commutative equations. Chapter 1 outlines some of the basic concepts of …
-
Generalized integral transforms related to the theory of potential and stokes flow
The main concern of this Dissertation is focused on the derivation of novel integral formulation for simple problems. This alternative integral representations display a rapid decay as the complex parameter involved tends to infinity and are therefore suitable for numerical computations and for the …