Analytical insights into three models: Exact solutions and nonlinear vibrations

Exact propagation without analytical solutions

We present a simulation algorithm that accurately propagates a molecule pair using large time steps without the need to invoke the full exact analytical solutions of the Smoluchowski diffusion equation. Because the proposed method only uses uniform and Gaussian random numbers, it allows for position updates that are two to three orders of magnitude faster than those of a corresponding scheme ba...

Exact solutions of nonlinear interval Volterra integral equations

Exact classical solutions of nonlinear sigma models on supermanifolds

We study two-dimensional nonlinear sigma models with target spaces being the complex super Grassmannian manifolds, that is, coset supermanifolds G(m, p|n, q) ∼= U(m|n)/[U(p|q) ⊗ U(m − p|n − q)] for 0 ≤ p ≤ m, 0 ≤ q ≤ n and 1 ≤ p + q. The projective superspace CP is a special case of p = 1, q = 0. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmoni...

Exact solutions of (3 +1)-dimensional nonlinear evolution equations

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

Analytical Solutions of Exact Renormalization Group Equations

We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second order phase transitions, critical exponents, first order transitions (som...