Related papers: Generalized solutions for inextensible string equa…
We study a fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators. The iterative method is assembled by averaging of strings, and each string is composed of finitely many strictly…
We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients…
We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple…
We study the three-dimensional incompressible Euler equations subject to stochastic forcing. We develop a concept of dissipative martingale solutions, where the nonlinear terms are described by generalised Young measures. We construct these…
The loop variable approach used earlier to obtain free equations of motion for the massive modes of the open string, is generalized to include interaction terms. These terms, which are polynomial, involve only modes of strictly lower mass.…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
We consider 1+4 dimensional black string solutions which are invariant under translation along the fifth direction. The solutions are characterized by the two parameters, mass and tension, of the source. The Gregory-Laflamme solution is…
We investigate the long time behaviour of the $L^2$-energy of solutions to wave equations with variable speed. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation…
We study a system of nonlinear partial differential equations describing the unsteady motions of incompressible chemically reacting non-Newtonian fluids. The system under consideration consists of the generalized Navier-Stokes equations…
The loop variable approach is a proposal for a gauge invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space-time gauge invariance…
We study the space-time invariances of the bosonic relativistic particle and bosonic relativistic string using general formulations obtained by incorporating the Hamiltonian constraints into the formalism. We point out that massless…
The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the…
In this paper we consider new solutions for pulsating strings. For this purpose we use tha idea of the generalized ansatz for folded and circular strings in hep-th/0311004. We find the solutions to the resulting Neumann-Rosochatius…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
We evaluate gauge invariants, action and gauge invariant overlap, for numerical solutions which satisfy the "a-gauge" condition with various values of $a$ in cubic open bosonic string field theory. We use the level truncation approximation…
We derive the equations of motion for general strings, i.e. strings with arbitrary relation between tension $\tau$ and energy per unit length $\epsilon$. The renormalization of $\tau$ and $\epsilon$ that results from averaging out small…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon…
We construct exact non-perturbative massive solutions in the gravitational Higgs mechanism. They confirm the conclusions of arXiv:1102.4991, which are based on non-perturbative Hamiltonian analysis for the relevant metric degrees of…