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In this paper, Quasinormal modes of gravitational perturbation are investigated for the regular Bardeen black hole surrounded by quintessence. Considering the metric of the Bardeen spacetime surrounded by quintessence, we derived the perturbation equation for gravitational perturbation using Regge-Wheeler gauge. The third order WentzelKramers-Brillouin (WKB) approximation method is used to evaluate quasinormal frequencies. Explicitly, the behaviors of the black hole potential and quasinormal modes were plotted. The results show that, due to the presence of quintessence, the gravitational perturbation around the black hole damps more slowly and oscillates more slowly.

In this paper, thermodynamics and phase transition are investigated for the regular Bardeen black hole. Considering the metric of the Bardeen spacetime, we derived the Unruh-Verlinde temperature. Using the first law of thermodynamics, we derived the expression of the specific heat and plot its behavior. It results that the magnetic monopole charge β reduces the temperature and induces a thermodynamics phase transition in the spacetime. Moreover, when increasing β, the transition point moves to higher entropy.

We consider a new equation recently found by Schäfer and Wayne, hereafter named Schäfer–Wayne short pulse equation (SWSPE), describing the propagation of an ultrashort pulse in nonlinear media. Using some vanishing boundary conditions, we construct and discuss the N-soliton solutions to the previous equation by means of the Wadati–Konno–Ichikawa (WKI) method, which is arguably more direct than the map through the sine-Gordon equation investigated much earlier by Sakovich and Sakovich (2005 J. Phys. Soc. Japan 74 239, 2006 J. Phys. A: Math. Gen. 39 L361). We particularly focus our attention on the two-soliton solution as an application. As a result, the collision process for two-soliton solutions with ‘similar’ amplitudes exhibits very different behaviour from the case when the amplitudes are ‘dissimilar’.

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