In this work we study single, double, and triple heavy-flavor baryons using the hypercentral approach in the framework of the non-relativistic quark model. Considering two different confining potentials and an improved form of the hyperfine interaction, we calculate the ground-state masses of heavy baryons and also the ground-state magnetic moments of single charm and beauty baryons with J P = 3/2 + . The obtained results are in good agreement with experimental data and those of other works.

We consider an integrable equation governing short waves in a longwave model, derived recently by Faquir et al. [M.J. Faquir, M.A. Manna, A. Neveu, Proc. R. Soc. A463, 1939 (2007)]. The study is conducted in presence of perturbation terms. The perturbation terms that are considered are non-linear dispersion terms and fourth order dispersion. The solitary wave Ansatz is used to carry out the integration of the considered perturbed evolution equation. Both bright and dark solitons solutions are obtained. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The conditions of the existence of the derived solitons are derived.

The masses of the ground state heavy baryons are studied using the hypercentral approach. The considered potential is a combination of Coulombic, linear confining and harmonic oscillator terms. An improved form of the hyperfine interaction and isospin dependent quark potential is introduced. By solving the Schrödinger equation for three particles system, we calculate the ground state masses of the baryons containing one, two and three heavy quarks. The obtained results are very close to the ones obtained in experiments or in the other works.

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