Related papers: Inverse Scattering and the Geroch Group
STU supergravity becomes an integrable system for solutions that effectively only depend on two variables. This class of solutions includes the Kerr solution and its charged generalizations that have been studied in the literature. We here…
The Riemann-Hilbert approach to studying solutions of supergravity theories allows us to associate spacetime independent monodromy matrices (matrices in the Geroch group) with solutions that effectively only depend on two spacetime…
On one hand the Geroch group allows one to associate spacetime independent matrices with gravitational configurations that effectively only depend on two coordinates. This class includes stationary axisymmetric four- and five-dimensional…
The inverse scattering problem method application to construction of exact solution for Maxwell dilaton gravity system ia considered. By use of Belinsky and Zakharov L - A pair the solution of the theory is constructed. The rotating Kerr -…
Geroch's solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector {{}and are thus asymptotically (locally) (anti-)de Sitter}. This includes the reduction to a three-dimensional coset space, the…
A class of negative order Ablowitz--Kaup--Newell--Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of the first order linear system of three equations. The inverse scattering problem on the whole axis are…
We give a solution of the Inverse Scattering Problem for integrable systems with a finite number degrees of freedom, admitting a Lax representation with spectral parameter on a Riemann surface. While conventional approaches deal with the…
We study stationary and axially symmetric two solitonic solutions of five dimensional vacuum Einstein equations by using the inverse scattering method developed by Belinski and Zakharov. In this generation of the solutions, we use five…
The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable,…
A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a non-flat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find…
In this paper the well known Belinskii and Zakharov soliton generating transformations of the solution space of vacuum Einstein equations with two-dimensional Abelian groups of isometries are considered in the context of the so called…
It is well known that, for even n, the n-soliton solution on the Minkowski seed, constructed using the inverse-scattering method (ISM) of Belinski and Zakharov (BZ), is the multi-Kerr-NUT solution. We show that, for odd n, the natural seed…
We consider a certain first-order linear system of ordinary differential equations, and we analyze the direct and inverse scattering problems for that linear system. The linear system involves two potentials in the Schwartz class, and those…
Extending the single-angular-momentum case analyzed in our previous work, we investigate the solution-generating technique based on the Breitenlohner-Maison (BM) linear system for asymptotically flat, stationary, bi-axisymmetric black hole…
We construct new integrable systems describing particles with internal spin from four-dimensional $\mathcal{N}=2$ quiver gauge theories. The models can be quantized and solved exactly using the quantum inverse scattering method and also…
Within the framework of the Riemann-Hilbert problem, the theory of inverse scattering transform is established for the defocusing nonlinear Schr\"{o}dinger equation with local and nonlocal nonlinearities (which originates from the…
Kinnersley--type representation is constructed for the four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times possessing two non--null commuting Killing symmetries. New representation essentially uses the…
The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the…
We explore the integrability of five-dimensional minimal supergravity in the presence of three commuting Killing vectors. We argue that to see the integrability structure of the theory one necessarily has to perform an Ehlers reduction to…
We investigate Lie symmetry algebra of the Benney-Roskes/Zakharov-Rubenchik systems. The invariance algebra turns out to be infinite-dimensional. We also find several exact solutions of periodic, line-soliton and stationary types.