相关论文: Perturbation theory for nearly integrable multi-co…
It was recently demonstrated that time-dependent PDE problems can numerically be solved with a fully pseudospectral scheme, i.e. using spectral expansions with respect to both spatial and time directions (Hennig and Ansorg, 2009 [15]). This…
A selfconsistent system of equations describing evolution of linear spherically symmetric perturbations in Fridmann world by an arbitrary equation of state is obtained. The perturbations singular part corresponding to massive particle-like…
The set of integrable symmetries of the nonstationary Schr\"{o}dinger equation is shown to admit a natural decomposition into subsets of mutually commuting symmetries. Hierarchies of time evolutions associated with each of these subsets…
Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution…
We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by…
We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…
We give the solution of certain parabolic evolution problems (time-depending perturbations of the heat equation for the harmonic oscillator) as explicit integrals on the Wiener space.
We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark…
We consider perturbations of the non-unitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of non-integrable singularities in the resulting theories leads to constraints on the…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological N-body…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general…
Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows…
In \cite{LZ2} it is proved that for certain class of perturbations of the hyperbolic equation $u_t=f(u) u_x$, there exist changes of coordinate, called quasi-Miura transformations, that reduce the perturbed equations to the unperturbed one.…
We investigate the effect of the breaking of integrability in the integrals of motion of a sine-Gordon-like system. The class of quasi-integrable models, discussed in the literature, inherits some of the integrable properties they are…
In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signal that can be observed. Beyond the spatial distributions of astronomical objects, the spatial…
We develop new perturbative tools to accurately study radiatively-induced first-order phase transitions. Previous perturbative methods have suffered internal inconsistencies and been unsuccessful in reproducing lattice data, which is often…
We consider semilinear stochastic evolution equations on Hilbert spaces with multiplicative Wiener noise and linear drift term of the type $A + \varepsilon G$, with $A$ and $G$ maximal monotone operators and $\varepsilon$ a "small"…