2,802 research outputs found

### On the equation of the $p$-adic open string for the scalar tachyon field

We study the structure of solutions of the one-dimensional non-linear
pseudodifferential equation describing the dynamics of the $p$-adic open string
for the scalar tachyon field $p^{\frac12\partial^2_t}\Phi=\Phi^p$. We elicit
the role of real zeros of the entire function $\Phi^p(z)$ and the behaviour of
solutions $\Phi(t)$ in the neighbourhood of these zeros. We point out that
discontinuous solutions can appear if $p$ is even. We use the method of
expanding the solution $\Phi$ and the function $\Phi^p$ in the Hermite
polynomials and modified Hermite polynomials and establish a connection between
the coefficients of these expansions (integral conservation laws). For $p=2$ we
construct an infinite system of non-linear equations in the unknown Hermite
coefficients and study its structure. We consider the 3-approximation. We
indicate a connection between the problems stated and the non-linear
boundary-value problem for the heat equation.Comment: AMSTeX, 26 page

### Nonlinear equations for p-adic open, closed, and open-closed strings

We investigate the structure of solutions of boundary value problems for a
one-dimensional nonlinear system of pseudodifferential equations describing the
dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar
tachyon field using the method of successive approximations. For an open-closed
string, we prove that the method converges for odd values of p of the form
p=4n+1 under the condition that the solution for the closed string is known.
For p=2, we discuss the questions of the existence and the nonexistence of
solutions of boundary value problems and indicate the possibility of
discontinuous solutions appearing.Comment: 16 pages, 3 figure

### On the Nonlinear Dynamical Equation in the p-adic String Theory

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 in mathematical physics and its applications in particular in string
theory and cosmology.
In the present work a systematical mathematical investigation of the
properties of these equations is performed. The main theorem of uniqueness in
some algebra of tempored distributions is proved. Boundary problems for bounded
solutions are studied, the existence of a space-homogenous solution for odd p
is proved. For even p it is proved that there is no continuous solutions and it
is pointed to the possibility of existence of discontinuous solutions.
Multidimensional equation is also considered and its soliton and q-brane
solutions are discussed.Comment: LaTex, 18 page

### Noncommutative magnetic moment of charged particles

It has been argued, that in noncommutative field theories sizes of physical
objects cannot be taken smaller than an elementary length related to
noncommutativity parameters. By gauge-covariantly extending field equations of
noncommutative U(1)_*-theory to the presence of external sources, we find
electric and magnetic fields produces by an extended charge. We find that such
a charge, apart from being an ordinary electric monopole, is also a magnetic
dipole. By writing off the existing experimental clearance in the value of the
lepton magnetic moments for the present effect, we get the bound on
noncommutativity at the level of 10^4 TeV.Comment: 9 pages, revtex; v2: replaced to match the published versio

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