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 investigate both analytically and numerically the localized multivalued waveguide channels-the loop solitons-dynamics within a ferrite slab. In the starting point of the work, we solve in detail the initial value problem of the system while unveiling the existence of multivalued waveguide channels solutions. Paying particular interest to the nonlinear scattering among these excitations, we study extensively the different kinds of interacting features between these localized waves alongside the depiction of their energy densities. As a result, we find that the interactions can be attractive or repulsive depending strongly on the ratio of the amplitudes of the interacting structures. In the wake of these results, we address some physical implications, accordingly.

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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In this work, we investigate the dynamics of an uniaxial silica fiber under the viewpoint of propagation of ultimately ultrashort optical waveguide channels. As a result, we unveil the existence of three typical kinds of ultrabroadband excitations whose profiles strongly depend upon their angular momenta. Looking forward to surveying their scattering features, we unearth some underlying head-on scenarios of elastic collisions. Accordingly, we address some useful and straightforward applications in nonlinear optics through secured data transmission systems, as well as laser physics and soliton theory with optical soliton dynamics.