A two-loop soliton solution to the Schäfer-Wayne short-pulse equation (SWSPE) is shown. The key step in finding this solution is to transform the independent variables in the equation. This leads to a transformed equation for which it is straightforward to find an explicit two-soliton solution using Hirota's method. The two-loop soliton solution to the SWSPE is then found in implicit form by means of a transformation back to the original independent variables. Following Hodnett and Moloney's approach, some computations of the energy of the one-and two-soliton solutions are made.

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In this paper, we review basic results, essentially due to J. Turiel, concerning the link between classical multidimensional webs and Veronese webs.

In the wake of the recent investigation of new coupled integrable dispersionless equations by means of the Darboux transformation [Zhaqilao, et al., Chin. Phys. B 18 (2009) 1780], we carry out the initial value analysis of the previous system using the fourth-order Runge-Kutta's computational scheme. As a result, while depicting its phase portraits accordingly, we show that the above dispersionless system actually supports two kinds of solutions amongst which the localized traveling wave-guide channels. In addition, paying particular interests to such localized structures, we construct the bilinear transformation of the current system from which scattering amongst the above waves can be deeply studied.

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Abstract. The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are non-trivial and not yet completely understood. In this paper we consider the occupation time T + of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments of T + analytically and also study the statistics of T + with Monte Carlo simulations. One goal of our work was to ascertain whether the occupation time T + and the time T m at which the maximum of the process is attained are statistically equivalent. For regular Brownian motion the distributions arXiv:1603.06883v3 [cond-mat.stat-mech] 5 May 2016Occupation time statistics of the random acceleration model 2 of T + and T m coincide and are given by Lévy's arcsine law. We show that for randomly accelerated motion the distributions of T + and T m are quite similar but not identical. This conclusion follows from the exact results for the moments of the distributions and is also consistent with our Monte Carlo simulations.PACS numbers: 05.40.Fb,