Related papers: String equation--2. Physical solution

We consider {\em discretized} Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular nonlinear part. We consider splitting methods associated with this decomposition. Using a…

We study general properties of the classical solutions in non-polynomial closed string field theory and their relationship with two dimensional conformal field theories. In particular we discuss how different conformal field theories which…

The static kink, sphaleron and kink chain solutions for a single scalar field $\phi$ in one spatial dimension are reconsidered. By integration of the Euler--Lagrange equation, or through the Bogomolny argument, one finds that each of these…

We consider the symmetry-breaking steady state bifurcation of a spatially-uniform equilibrium solution of E(2)-equivariant PDEs. We restrict the space of solutions to those that are doubly-periodic with respect to a square or hexagonal…

This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…

We present a simple physical representation for states of the two-dimensional string theory. In order to incorporate a fundamental cutoff of the order 1/g we use a picture consisting of q-oscillators at the first-quantized level. In this…

A second order ordinary differential equation with a superlinear term $g(x,u)$ under radiation boundary conditions is studied. Using a shooting argument, all the results obtained in a previous work for a Painlev\'e II equation are extended.…

A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential…

A class of exactly solvable string models can be obtained by starting with flat space and combining T-duality and shifts of angular coordinates of several polar planes. The models are the analog of the Lunin-Maldacena \beta-deformation of…

Let $(1) Rh=f$, $0\leq x\leq L$, $Rh=\int^L_0 R(x,y)h(y) dy$, where the kernel $R(x,y)$ satisfies the equation $QR=P\delta(x-y)$. Here $Q$ and $P$ are formal differential operators of order $n$ and $m<n$, respectively, $n$ and $m$ are…

In this paper, we search for normalized solutions to a fractional, nonlinear, and possibly strongly sublinear Schr\"odinger equation $$(-\Delta)^s u + \mu u = g(u) \quad \hbox{in $\mathbb{R}^N$},$$ under the mass constraint…

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used in the equation, which permits to evaluate the wave-function normalization after the…

We are considering the semi-classical string soliton solution of Gubser, Klebanov and Polyakov which represents highly excited states on the leading Regge trajectory, with large spin in $AdS_5$. A prescription relates this soliton solution…

We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that the solution is non-trivial if and only if corresponding…

We prove that for every separately twice differentiable solution $f$ of the PDE $f"_{xx}=f"_{yy}$ is of the form $f(x,y)=\phi(x+y)+\psi(x-y)$ for some twice differentiable functions $\phi, \psi$.

A bivariate spline method is developed to numerically solve second order elliptic partial differential equations (PDE) in non-divergence form. The existence, uniqueness, stability as well as approximation properties of the discretized…

We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N =4 Super Yang-Mills. The…

In this work, a solution linear in the momentum for the massless constraint $P^{m}P_{m}=0$ is investigated. It is presented in terms of a $SO(2n,\mathbb{C})$ to $U(n)$ decomposition and interpreted in terms of projective pure spinors, which…

We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations. The main idea is to apply the…

We perform a first principle semiclassical quantisation of the general finite-gap solution to the equations of a string moving on R x S^3. The derivation is only formal as we do not regularise divergent sums over stability angles. Moreover,…