ON THE EQUATION OF THE p -ADIC OPEN STRING FOR THE SCALAR TACHYON FIELD
نویسندگان
چکیده
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 1 2 ∂ t Φ = Φ. We elicit the role of real zeros of the entire function Φ(z) and the behaviour of solutions Φ(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 Φ and the function Φ 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. §
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