1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity
Abstract This paper obtains the 1-soliton solution of the Jaulent–Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence.
Separability and dynamical r-matrix for the constrained flows of the Jaulent-Miodek hierarchy
Abstract We show the separability of the Hamilton-Jacobi equation for a hierarchy of integrable Hamiltonian systems obtained from the constrained flows of the Jaulent-Miodek hierarchy. The classical Poisson structure for these Hamiltonian systems is constructed. The associated r -matrices depend not only on the spectral parameters, but also on the dynamical variables and, for consistency, have to obey the classical Yang-Baxter equations of dynamical type. Some new solutions of classical dynamical Yang-Baxter equations are presented. Thus these integrable systems provide examples both for the dynamical r -matrix and for the separable Hamiltonian system not having a natural Hamiltonian form.
5.63 and 5.80 MeV levels of Ne20; de-excitation branching
Abstract The ratio Г γ /Г for the 5.63 and 5.80 MeV levels of Ne 20 has been determined to be 0.077 (±0.008) and −4 , respectively, by using the C 12 (C 12 , α)Ne 20 reaction and determining the fraction of the events in which the alpha-particle and the Ne 20 recoil are present in coincidence at the kinematically correct angles. In both cases these results in themselves are shown to imply radiative E1 transition (5.63→1.63 and 5.80→0, respectively) probabilities ⪡5 × 10 −5 Weisskopf units. When taken together with the life-time for the 5.63 MeV level measured by Evans et al . values of Г( E1 ) ≲ 5 × 10 −6 and Г α ≈ 6% of the particle estimate are obtained for this state.