abstract

We study higher-order rogue wave patterns for the well-known Boussinesq equation for the cases where the solution parameters are large. We show that these consist of a collection of individual fundamental rogue waves arranged in circles. The radii of these circles are found from the zeroes of certain polynomials. Finally, we briefly compare the patterns found with those of higher-order rogue wave patterns of the nonlinear-Schrödinger (NLS) and other equations.

abstract

The first-forbidden \(\Delta J=0\), \(\pm 2\) transitions are analyzed by using a self-consistent effective potential within the framework of proton–neutron quasi-particle random phase approximation (pn-QRPA) method. The self-consistency arises from the fact that the particle–hole and particle–particle strength parameters can be found analytically within the present approximation. The beta (\(\beta \)) decay matrix elements and log\(ft\) values are computed and compared with the corresponding experimental data. The present approximation is usually successful in reproducing the experimental data.

abstract

We investigate a manifestation of low-energy dipole collectivity in heavy nuclei, known as clustering, using algebraic techniques. In the first step, the connection of the nuclear vibron model to the U(10) algebra (spanned by four types of bosons, within the interacting boson model I (IBM-I)) is extended to other possible models through a detailed study of the U(10) subalgebras. Subsequently, the ability of the vibron model to reproduce the experimental data is extended to a wider region of heavy nuclei belonging to the rare-earth and actinide regions. A more realistic irrep labelling has been introduced to take into account the Wildermuth condition. In a second step, we upgrade the model to the IBM-II level involving the U(20) algebra, where a new \(G\)-spin and hybrid limits have been introduced.