32 research outputs found
Recursive generation of isochronous Hamiltonian systems
We propose a simple procedure to identify the collective coordinate Q which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscillators, recursively
A Linear Approximation for the Excitation Energies of single and double analog states in the f_{7/2} shell
We find that the excitation energies of single analog states for odd-even
nuclei in the f shell with J=j=7/2 and the J=0 double
analog states in the even-even nuclei are well described by the formulas
and ,respectively,
where is usually the ground state isospin. It is remarkable
to note that the parameter X accounts for the departures from the symmetry
energy based predictions.Comment: 8 pages and no figure
Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation
We consider the nonlinear Helmholtz (NLH) equation describing the beam
propagation in a planar waveguide with Kerr-like nonlinearity under
non-paraxial approximation. By applying the Lie symmetry analysis, we determine
the Lie point symmetries and the corresponding symmetry reductions in the form
of ordinary differential equations (ODEs) with the help of the optimal systems
of one-dimensional subalgebras. Our investigation reveals an important fact
that in spite of the original NLH equation being non-integrable, its symmetry
reductions are of Painlev\'e integrable. We study the resulting sets of
nonlinear ODEs analytically either by constructing the integrals of motion
using the modified Prelle-Singer method or by obtaining explicit travelling
wave-like solutions including solitary and symbiotic solitary wave solutions.
Also, we carry out a detailed numerical analysis of the reduced equations and
obtain multi-peak nonlinear wave trains. As a special case of the NLH equation,
we also make a comparison between the symmetries of the present NLH system and
that of the standard nonlinear Schr\"odinger equation for which symmetries are
long available in the literature.Comment: Accepted for publication in "Applied Mathematics and Computation". 18
pages, 15 figure