Related papers: String equation--2. Physical solution

The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential…

In this work nonlinear pseudo-differential equations with the infinite number of derivatives are studied. These equations form a new class of equations which initially appeared in p-adic string theory. These equations are of much interest…

It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity…

We apply non-linear WKB analysis to the study of the string equation. Even though the solutions obtained with this method are not exact, they approximate extremely well the true solutions, as we explicitly show using numerical simulations.…

For conformal maps defined in the unit disk one can define a certain Poisson bracket that involves the harmonic moments of the image domain. When this bracket is applied to the conformal map itself together with its conformally reflected…

String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…

String Theory is the result of the conjunction of three conceptually independent elements: (i) the metaphysical idea of a nomological unity of the forces, (ii) the model-theoretical paradigm of Quantum Field Theory, and (iii) the conflict…

We find exact solutions of the string equations of motion and constraints describing the {\em classical}\ splitting of a string into two. We show that for the same Cauchy data, the strings that split have {\bf smaller} action than the…

The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutions of DP1 are classified under criterion of their behavior while argument tends to infinity. The Isomonodromic Deformations Method yields asymptotic…

The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…

A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…

We analyze the asymptotic properties a special solution of the $(3,4)$ string equation, which appears in the study of the multicritical quartic $2$-matrix model. In particular, we show that in a certain parameter regime, the corresponding…

We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…

In this paper, we are concerned with stable solutions , possibly unbounded and sign-changing, of some semi-linear elliptic problem with mixed nonlinear boundary conditions. We establish the nonexistence of stable solutions, the main methods…

In this work some nonlinear integral equation is studied. This equation has arisen in the (super)string field theory and cosmology. In this work it is proved that some boundary problem for this equation has a solution.

We consider the nonlinear string equation with Dirichlet boundary conditions $u_{xx}-u_{tt}=\phi(u)$, with $\phi(u)=\Phi u^{3} + O(u^{5})$ odd and analytic, $\Phi\neq0$, and we construct small amplitude periodic solutions with frequency…

We present the general solution of the system of coupled nonlinear equations describing dynamics of $D$--dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and…

We present a brief survey of the results of the Theory of Solitons from the viewpoint of the periodic theory including some new results in the theory of 2-dimensional periodic Schrodinger Operators. The main subjects are: Periodic Solitons…

We find solutions of Einstein's field equation for topologically stable strings associated with the breaking of a U(1) symmetry. Strings form in many GUTs and are expected whenever the homotopy group $\Pi_1(M_0)$ is non-trivial. The…

{\bf Exact} solutions of the string equations of motion and constraints are {\bf systematically} constructed in de Sitter spacetime using the dressing method of soliton theory. The string dynamics in de Sitter spacetime is integrable due to…