In this paper we investigate the correspondence between the Da Rios-Betchov equation, which appears in the three-dimensional motion of a vortex filament, and the nonlinear Schrödinger equation. Using this correspondence we map a set of solutions corresponding to breathers in the nonlinear Schrödinger equation to waves propagating along a vortex filament. The work presented generalizes the recen...

In this article, nonlinear propagation of envelope gravity waves is studied in baroclinic atmosphere. The classical (2 + 1) dimensional nonlinear Schrödinger (NLS) equation can be derived by using the multiple-scale, perturbation method. Further, via the semi-inverse method, the Euler–Lagrange equation and Agrawal’s method, the time–space fractional (2 + 1) dimensional nonlinear Schrödinger (FN...

The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of bi-Hamiltonian methods in [A. S. Fokas, Phys. D 87 (1995), 145–150]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as...

In this paper we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schrödinger equation with constant coefficients. This allows us to prove dispersive estimates, which in turn are useful for solving the nonlinear Schrödinger equation. The proof extends also to...

Using a traveling wave reduction technique, we have shown that Maccari equation, (2?1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3?1)-dimensional modified KdV–Zakharov– Kuznetsev equation, (2?1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equ...

We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schrödinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the averaged cubic-quintic nonlinear Schrödinger (NLS) equation and modified variational approach for the arrest of collapse coincide. The analytical results are c...