abstract

This paper investigates the generalized Fokas–Lenells equation by the Riemann–Hilbert approach. A gauge transformation is introduced to symmetrize the originally asymmetric spectral problem. A novel Riemann–Hilbert method is developed for the generalized Fokas–Lenells equation, performing spectral analysis on the temporal component of the Lax pair rather than the spatial part. \(N\)-soliton solutions are rigorously derived by solving the Riemann–Hilbert problem with this complex spectral symmetry. Additionally, the dynamics of the one and two solitons of the generalized Fokas–Lenells equation are discussed.

abstract

The intrinsic level densities and entropies of \(^{210}\)Po and \(^{211}\)Po nuclei have been extracted within the BCS theory that includes pairing interaction. Then, total level density considering the collective effects is obtained. The results agree well with the recent data obtained from experimental-level densities for the considered nuclei. In addition, the entropy excess of \(^{211}\)Po compared to \(^{210}\)Po has been extracted. Also, the entropy excess ratio, which was introduced in our previous publications, has been calculated as a function of temperature for the neutrons and protons. The neutron system plays a major role in the entropy excess of \(^{211}\)Po at low temperatures.

abstract

We give a complete description of the representation of \(\mathrm {SL}(2,\mathbb {C})\) acting in the Hilbert space of the quantum Coulomb field and a constructive consistency proof of the axioms of the quantum theory of the Coulomb field.