Related papers: Tension as a Perturbative Parameter in Non--Linear…
String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension $\epsilon=\gamma/\alpha^{\prime}$, where $\gamma$ is a metric parametrizing constant. A rescaled slow…
We introduce N-parameter perturbation theory as a new tool for the study of non-linear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to…
An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable…
We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear…
An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
Treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh-Schrodinger power series. This power series is proved to be…
Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate…
We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1<z<6. We find that the perturbation theory prediction agrees with the simulations to better…
We derive a generalized equation for the evolution of tensor perturbations in a cosmological background, taking into account higher-curvature contributions and a tree-level coupling to the dilaton in the string frame. The equation is…
A covariant formalism for physical perturbations propagating along a string in an arbitrary curved spacetime is developed. In the case of a stationary string in a static background the propagation of the perturbations is described by a…
Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in…
For the case of tension tensor containing nonlinear terms in $l^{\alpha}$, we give generalization of Vilenkin metrics and equations of motion of cosmic string. Dynamics of nonlinear string in (1+1)-dimensional universe is discussed.
A perturbation theory for the Nonlinear Schroedinger Equation (NLSE) in 1D on a lattice was developed. The small parameter is the strength of the nonlinearity. For this purpose secular terms were removed and a probabilistic bound on small…
String dynamics near the photon sphere in Schwarzschild spacetime is considered on the basis of a perturbative approach with respect to a rescaled string tension as a small parameter. The perturbative string solution in the zeroth and first…
The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the…
A class of non-supersymmetric string backgrounds can be constructed using twists that involve space-time fermion parity. We propose a non-perturbative definition of string theory in these backgrounds via gauge theories with supersymmetry…
Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes,…
We develop a non-linear framework for describing long-wavelength perturbations in multiple-field inflation. The basic variables describing inhomogeneities are defined in a non-perturbative manner, are invariant under changes of time slicing…