We derive analytical 3D spatiotemporal similaritons and solitons of the generalized (3+1)-dimensional nonlinear Schrodinger equation with distributed coefficients.

Analytical spatiotemporal localizations for the generalized (3+1)-dimensional nonlinear Schrödinger equation.

We analytically obtain both bright and dark spatial similaritons on the background wave and rogons in two-dimensional (2D) graded-index waveguides.

Exact spatial similaritons and rogons in 2D graded-index waveguides.

Quasi-two-dimensional Bose-Einstein condensates with spatially modulated cubic-quintic nonlinearities

E. Sanchez-Palencia In this paper, we investigate the dynamic of DNA described via DNA double-stranded model with transverse and longitudinal motions. This model admits solitary, soliton, periodic, or chirped wave solution. It is justified that the most admissible physical solution is the soliton or chirped wave solution. The stability analysis of all these solutions is performed by using the Sturm–Liouville problem and the topological invariance. We found that soliton and chirped waves are unstable so that the unbounded amplitude may occur. In the view of these models, damage of DNA membrane or bases may occur under small disturbance. Also, the suggested models will be indispensable when inhomogeneity or medium dissipation is taken into account. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic of DNA's possible impact on its damage

A large family of analytical solitary wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schr\"odinger equation with time- and space-dependent distributed coefficients and external potentials are obtained by using a similarity transformation technique. We use the cubic nonlinearity as an independent parameter function, where a simple procedure is established to obtain different classes of potentials and solutions. The solutions exist under certain conditions and impose constraints on the coefficients depicting dispersion, cubic and quintic nonlinearities, and gain (or loss). We investigate the space-quadratic potential, optical lattice potential, flying bird potential, and potential barrier (well). Some interesting periodic solitary wave solutions corresponding to these potentials are then studied. Also, properties of a few solutions and physical applications of interest to the field are discussed. Finally, the stability of the solitary wave solutions under slight disturbance of the constraint conditions and initial perturbation of white noise is discussed numerically; the results reveal that the solitary waves can propagate in a stable way under slight disturbance of the constraint conditions and the initial perturbation of white noise.

Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials

Chirped and chirp-free self-similar cnoidal and solitary wave solutions of the cubic-quintic nonlinear Schrödinger equation with distributed coefficients

Caijie Yan

Papers

Chirped and chirp-free self-similar cnoidal and solitary wave solutions of the cubic-quintic nonlinear Schrödinger equation with distributed coefficients