Nonlinear approach in the ?-cluster model

Abstract

Abstract. Nonlinear Schroedinger Equation ( NoSE ) and Korteveg de Vries Equation ( KdVE ) are applied to the solving of problems of the nucleation and clustering. PACS: 21.65.+fIn last years more and more attention is being paid to problems connected with nonlinear equations and their solutions. The aim of the present contribution is to apply Nonlinear Schroedinger Equation (NOSE) and Korteveg de Vries Equation (KdVE) to an interpretation of some effects of the clustering in nuclei. Earlier we applied the NoSE for the explanation such phenomena as the ALAS (Anomalous Large Angular Scattering) in interactions of c>particles with light nuclei [1]. Also we used the NoSE for the description of c>particle spectra in2~ [2]. In both cases we exploitated the NoSE in such form:where C = K/9; here K-the compressibility constant. It turned out that (1) The certain amount e of energy per bit is expended, transferred, stored, associated with the information encoded. That's why it is necessary to add the term eI to the standard Hamiltonian:j=l Now it is possible to show that this constant e is very close to our compressibility constant. The total energy as the expectation value of the Hamiltonian (2) is: = E0e < ~) I log2(a t ~ [ 2) I if) >