The wave propagation on an ocean or water surface in the presence of sea ice or surface tension is of current importance. In this paper, we investigate the (2 + 1) dimensional 6th-order model proposed recently by Hărăgus-Courcelle and Il’ichev for such wave propagation. Firstly, we correct...

Currently, the variable-coefficient nonlinear Schrödinger (NLS)-typed models have attracted considerable attention in such fields as plasma physics, nonlinear optics, arterial mechanics and Bose-Einstein condensates. Motivated by the recent work of Tian et al. [Eur. Phys. J. B <Emphasis Type="Bold">47, 329 (2005)],...</emphasis>

Describing space and laboratory plasmas, arterial mechanics and optical fibers, a generalized variable-coefficient nonlinear Schrödinger model is hereby under investigation. Four transformations have been constructed from such a model to the known standard and cylindrical nonlinear Schrödinger...

In this paper, we investigate the nonlinear dynamics of a Heisenberg spin chain with an external time-oscillating magnetic field. Such dynamics can be described by a Landau–Lifshitz-type equation. We apply the Darboux transformation method to the linear eigenvalue problem associated with this...

In this paper, the N-fold Darboux transformation is applied to the Lax pair associated with the (2+1)-dimensional nonlinear Schrödinger hierarchy. The general explicit formula for N-soliton solution is derived in terms of Vandermonde-like determinant expression. On the zero background, two...

Governing the simultaneous propagation of N fields in optical fibers and plasmas, the inhomogeneous N-coupled nonlinear Schrödinger equations are, with symbolic computation, analytically investigated in this paper. As one of the important integrable properties, the explicit one- and...

In this paper, by virtue of symbolic computation, the investigation is made on a generalized variable-coefficient higher-order nonlinear Schrödinger equation with varying higher-order effects and gain or loss, which can describe the femtosecond optical pulse propagation in a monomode dielectric...