Related papers: Dynamical systems method (DSM) for general nonline…
We consider entire solutions to $L u= f(u)$ in $\RR^2$, where $L$ is a general nonlocal operator with kernel $K(y)$. Under certain natural assumtions on the operator $L$, we show that any stable solution is a 1D solution. In particular, our…
Dynamic structure factor (DSF) is important for understanding excitations in many-body physics; it reveals information about the spectral and spatial correlations of fluctuations in quantum systems. Collective phenomena like quantum phase…
A two dimensional Finsler space associated with the differential equation $y''=Y_3 y'^3+Y_2 y'^2+Y_1 y'+Y_0$ is characterized by a tensor equation and called the Douglas space. An application to the Lorenz nonlinear dynamical equation is…
In this paper we consider the system involving fully nonlinear nonlocal operators: $$ \left\{ \begin{array}{ll} F_{\alpha}(u(x)) = C_{n,\alpha} PV \int_{{R}^n} \frac{G(u(x)-u(y))}{|x-y|^{n+\alpha}} dy=f(v(x)), F_{\beta}(v(x)) = C_{n,\beta}…
In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations (DNS) by solving the equations that govern the statistics themselves. DSS…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
Static spherically symmetric (SSS) solutions of f(R) gravity are studied in the Einstein frame. The solutions involve SSS configuration mass M and scalaron mass $\mu$ (in geometrized units); for typical astrophysical masses, the…
A globally converging numerical method to solve coupled sets of non-linear integral equations is presented. Such systems occur e.g. in the study of Dyson-Schwinger equations of Yang-Mills theory and QCD. The method is based on the knowledge…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates…
In this paper a second order dynamical system model is proposed for computing a zero of a maximal comonotone operator in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of a strong global solution of the proposed…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
A theorem on the solutions of the problem $U'(w)=\gamma F(U(w),w),\ U(w_1)=u_2,\ U(w_2)=u_2$ is applied for finding the functional solutions of the system of partial differential equations \begin{equation} \nabla\cdot(a(u,w)\nabla u)=0,\…
A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is…
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…