Dimitri Tsoubelis | University of Patras (original) (raw)

Papers by Dimitri Tsoubelis

Partial Differential Equations Riemann-Hilbert formulation for the KdV equation on a finite interval

Study of a Bianchi type-V cosmological model with torsion

Physical Review D, 1982

ABSTRACT

Pair creation and decay of a massive particle near and far away from a cosmic string

Physical Review D, 1992

We study the total transition probabilities of the tree-level processes of the pair creation and ... more We study the total transition probabilities of the tree-level processes of the pair creation and decay of a massive particle for real Klein-Gordon fields in the spacetime of an infinite straight static cosmic string. Basing the discussion on cylindrical modes characterized by an approximate radius of closest approach rmin, it is possible to approximately localize the non-Minkowskian processes to cylindrical effective interaction regions around the cosmic string. A physical understanding of the space dependence of the transition probabilities is obtained on the basis of analytic expressions for different energy domains referring to regions close to and far away from the string. For pair creation the Compton wavelength lambdaC of the created particles proves to be a crucial length scale. For rmin<<lambdaC the creation probability is insensitive to a variation of rmin. For large rmin it falls off at least exponentially with rmin. This agrees with an alternative ``integrated'' approach to localization: the cross section around the cosmic string is proportional to the Compton wavelength lambdaC. The decay of the massive particle on the other hand contains processes allowed in Minkowski spacetime and leads to another type of local behavior.

Journal of Physics A: Mathematical and Theoretical, 2007

We consider lattice equations on Z 2 which are autonomous, affine linear and possess the symmetri... more We consider lattice equations on Z 2 which are autonomous, affine linear and possess the symmetries of the square. Some basic properties of equations of this type are derived, as well as a sufficient linearization condition and a conservation law. A systematic analysis of the Lie point and the generalized three-and five-point symmetries is presented. It leads to the generic form of the symmetry generators of all the equations in this class, which satisfy a certain non-degeneracy condition. Finally, symmetry reductions of certain lattice equations to discrete analogues of the Painlevé equations are considered.

Journal of Physics A: Mathematical and Theoretical, 2009

Continuously symmetric solutions of the Adler-Bobenko-Suris class of discrete integrable equation... more Continuously symmetric solutions of the Adler-Bobenko-Suris class of discrete integrable equations are presented. Initially defined by their invariance under the action of both of the extended three point generalized symmetries admitted by the corresponding equations, these solutions are shown to be determined by an integrable system of partial differential equations. The connection of this system to the Nijhoff-Hone-Joshi "generating partial differential equations" is established and an auto-Bäcklund transformation and a Lax pair for it are constructed. Applied to the H1 and Q1 δ=0 members of the Adler-Bobenko-Suris family, the method of continuously symmetric reductions yields explicit solutions determined by the Painlevé trancendents.

Journal of Physics: Conference Series, 2007

The Lie point symmetries of the Einstein vacuum equations corresponding to the Bondi form of the ... more The Lie point symmetries of the Einstein vacuum equations corresponding to the Bondi form of the line element are presented. Using these symmetries, we study reductions of the field equations, which might lead to new asymptotically flat solutions, representing gravitational waves emitted by an isolated source. This is referred to as Bondi's radiating metric, and β, γ, U and V represent functions depending only on u, r, and θ.

Complete Specification of Some Partial Differential Equations That Arise in Financial Mathematics

Journal of Nonlinear Mathematical Physics, 2009

ABSTRACT We consider some well-known partial differential equations that arise in Financial Mathe... more ABSTRACT We consider some well-known partial differential equations that arise in Financial Mathematics, namely the Black–Scholes–Merton, Longstaff, Vasicek, Cox–Ingersoll–Ross and Heath equations. Our central aim is to discover any underlying connections taking into account the Lie remarkability property of the heat equation. For a few of these equations there is a known connection with the heat equation through a coordinate transformation. We investigate further that connection with the help of modern group analysis. This is realized by obtaining the Lie point symmetries of these equations and comparing their algebras with that of the heat equation. For those with an algebra identical to that of the heat equation a systematic way is shown to obtain the coordinate transformation that links them: the Lie remarkability property is a direct consequence. For the rest this is achieved only in certain subcases.

Journal of Mathematical Physics, 1992

A new four-parameter class of exact solutions of Einstein's field equations is obtained, using th... more A new four-parameter class of exact solutions of Einstein's field equations is obtained, using the inverse scattering method of Belinsky and Zakharov. Its members represent the head-on collision of a variably polarized gravitational plane wave with one having constant polarization and, in general, different profile, or with an infinitely thin shell of null dust. In some of these models no curvature singularity develops along the future boundary of the region of interaction. In certain cases the singularity avoidance is the direct result of the noncollinear polarization of the waves involved in the collision.

Multiple-soliton solutions of Einstein’s equations

Journal of Mathematical Physics, 1989

ABSTRACT Using the Belinsky–Zakharov generating technique and a flat metric as a seed, two‐ and f... more ABSTRACT Using the Belinsky–Zakharov generating technique and a flat metric as a seed, two‐ and four‐soliton solutions of the Einstein vacuum equations for the cases of stationary axisymmetric, cylindrically symmetric, or plane symmetric gravitational fields are considered. Three‐ and five‐parameter classes of exact solutions are obtained, some of which are new.

On the gravitational interaction of plane symmetric clouds of null dust

Journal of Mathematical Physics, 1991

ABSTRACT Plane symmetric solutions of the Einstein field equations are considered, solutions that... more ABSTRACT Plane symmetric solutions of the Einstein field equations are considered, solutions that represent the collision of oppositely moving clouds of initially unidentified massless particles—clouds of ‘‘null dust.’’ In terms of specific examples it is shown that the corresponding Cauchy problem remains ambiguous even when the Riemann tensor is free of any kind of discontinuity. By solving the corresponding Einstein–Klein–Gordon and Einstein–Maxwell–Weyl field equations the ambiguity is resolved and space-time models are constructed representing, among others, various types of collisions between a pair of scalar wave pulses as well as of a pulse of electromagnetic waves with a cloud of neutrinos.

Journal of Mathematical Physics, 2001

A new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional ... more A new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional reduction of the anti-self-dual Yang-Mills equations, is presented. It represents a generalization of the Ernst-Weyl equation of General Relativity related to colliding neutrino and gravitational waves, as well as of the fourth order equation of Schwarzian type related to the KdV hierarchies, which was introduced by Nijhoff, Hone, and Joshi recently. An auto-Ba ¨cklund transformation of the new system is constructed, leading to a superposition principle remarkably similar to the one connecting four solutions of the KdV equation. At the level of the Ernst-Weyl equation, this Ba ¨cklund transformation and the associated superposition principle yield directly a generalization of the single and double Harrison transformations of the Ernst equation, respectively. The very method of construction also allows for revealing, in an essentially algorithmic fashion, other integrability features of the main subsystems, such as their reduction to the Painleve ´transcendents.

Journal of Computational and Applied Mathematics, 2009

Complete symmetry groups enable one to characterise fully a given differential equation. By consi... more Complete symmetry groups enable one to characterise fully a given differential equation. By considering the reversal of an approach based upon complete symmetry groups we construct new classes of differential equations which have the equations of Bateman, Monge-Ampère and Born-Infeld as special cases. We develop a symbolic algorithm to decrease the complexity of the calculations involved.

General Relativity and Gravitation, 1988

The gravitational field along the symmetry axis of the Kerr spacetime is examined. The equations ... more The gravitational field along the symmetry axis of the Kerr spacetime is examined. The equations of parallel transport along this axis are solved for the timelike geodesics case, and the corresponding tidal tensor is constructed.

General Relativity and Gravitation, 1989

A new three-parameter class of solutions to the Einstein vacuum equations is presented which repr... more A new three-parameter class of solutions to the Einstein vacuum equations is presented which represents the collision of a pair of gravitational plane waves. Depending on the choice of the parameters, one of the colliding waves has a smooth or unbounded wavefront, or it is a shock, or impulsive, or shock accompanied by an impulsive wave, while the second is any of the above types. A subfamily of the solutions develops no curvature singularity in the interaction region formed by the colliding waves. 1 Expanded version of a talk presented at the Third National Workshop on Recent Developments in Gravitation,

General Relativity and Gravitation, 1990

Using the Szekeres family of solutions of Einstein's equations, exact models describing the colli... more Using the Szekeres family of solutions of Einstein's equations, exact models describing the collision of plane gravitational waves with planar shells of null dust are constructed.

General Relativity and Gravitation, 1987

The motion of test particles in polar orbit about the source of the Kerr field of gravity is stud... more The motion of test particles in polar orbit about the source of the Kerr field of gravity is studied, using Carter's first integrals for timelike geodesics in the Kerr space-time. Expressions giving the angular coordinates of such particles as functions of the radial one are derived, both for the case of a rotating black hole as well as for that of a naked singularity.

Classical and Quantum Gravity, 1988

The weak, dominant and strong energy conditions are investigated for various kinds of imperfect f... more The weak, dominant and strong energy conditions are investigated for various kinds of imperfect fluids. In this context, attention has been given to the model of a collapsing or expanding sphere of shear-free fluid which conducts heat and radiates energy to infinity.

Plane gravitational waves colliding with shells of null dust

Classical and Quantum Gravity, 1989

ABSTRACT Exact models describing the collision of plane gravitational waves with planar shells of... more ABSTRACT Exact models describing the collision of plane gravitational waves with planar shells of null dust are constructed. This is done by considering those members of the Szekeres (1972) family of colliding plane-gravitational-wave solutions which admit distribution valued stress-energy tensors with support on null hypersurfaces. It is shown that this class of solutions contains not only the Dray and 't Hooft (1986) and Babala (1987) models, but also models of the collision between planar shells of null dust and gravitational plane waves of all types (shock, impulsive, and with a smooth wavefront).