Related papers: Nonlinear equations for p-adic open, closed, and o…
In this paper we study a new class of pseudo-differential equations on functions of two $p$-adic variables. It is proved that the correspondent Cauchy problem has a unique solution. Some properties of this solution are studied, in…
In this review we describe our current understanding of the properties of open string tachyons on an unstable D-brane or brane-antibrane system in string theory. The various string theoretic methods used for this study include techniques of…
The tachyon field of p-adic string theory is made noncommutative by replacing ordinary products with noncommutative products in its exact effective action. The same is done for the boundary string field theory, treated as the p -> 1 limit…
The boundary string field theory approach is used to evaluate the one-loop tachyon potential. We first discuss the boundary condition at the two boundaries on annulus diagram and then the exact form of corrected potentials at zero and high…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
New exact string solutions in non-constant background fields are found and it is shown that some of them are compatible with the boundary conditions for the open string - D-brane system. Extension of the constraint algebra is proposed and…
We study the solvability of $(p,q)$-Laplacian problems with nonlinear reaction terms and non-homogeneous Neumann boundary conditions. First, we provide a complete description of the spectrum of the eigenvalue problem involving the…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
Given a D-brane background in string theory (or equivalently boundary conditions in a two-dimensional conformal field theory), classical solutions of open string field theory equations of motion are conjectured to describe new D-brane…
The solution form of the system of nonlinear difference equations \begin{equation*} x_{n+1} = \frac{x_{n-k+1}^{p}y_{n}}{a y_{n-k}^{p}+b y_{n}},\ y_{n+1} = \frac{y_{n-k+1}^{p}x_{n}}{\alpha x_{n-k}^{p}+\beta x_{n}}, \quad n, p \in…
Closed string tachyons have long been somewhat mysterious. We note that there is often a regime in the classical moduli space in which one can systematically compute the effective action for such fields. In this regime, the tachyon is…
We study a simple model of p-adic closed and open strings. It sheds some light on the dynamics of tachyon condensation for both types of strings. We calculate the effect of static and decaying D-brane configurations on the closed string…
This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p-Laplacian, the indefinite nonlinearity, and depend on the real parameter $\lambda$. A special focus is…
We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes. Despite the fact that the string field theory action contains infinite number of time…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…
A general class of nonlocal cosmological models is considered. A new method for solving nonlocal Friedmann equations is proposed, and solutions of the Friedmann equations with nonlocal operator are presented. The cosmological properties of…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
Open string field theory in the level truncation approximation is considered. It is shown that the energy conservation law determines the existence of rolling tachyon solution. The coupling of the open string field theory action to a…
We consider a number of boundary value problems involving the $p$-Laplacian. The model case is $-\Delta_p u=V|u|^{p-2}u$ for $u\in W_0^{1,2}(D)$ with $D$ a bounded domain in ${\bf R}^n$. We derive necessary conditions for the existence of…