The possibility of physically relevant singular solutions of the nonlinear Schrödinger equation with sustained dissipation into the singularity is considered through numerical study of a nonlinear dissipative regularisation and its small dissipation limit. A new form of such dissipative...

We review a recent mean-field statistical model of self-organization in a generic class of focusing, nonintegrable nonlinear Schrödinger (NLS) equations. Such equations provide natural prototypes for nonlinear dispersive wave turbulence. The main conclusion of the theory is that the...

We consider a higher order nonlinear Schrödinger equation with third- and fourth-order dispersions, cubic–quintic nonlinearities, self steepening, and self-frequency shift effects. This model governs the propagation of femtosecond light pulses in optical fibers. In this paper, we investigate...

We propose a discrete model of alpha-helical proteins by taking into account dipole and quadrupole type molecular excitations. The interaction properties of multisolitons are studied both analytically and numerically. We investigate the conditions for the modulation instability (MI) of plane...

With regards to the nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro, and Tsallis (NRT), based on Tsallis q-thermo-statistical formalism, we investigate the existence and properties of its quasi-stationary solutions, which have the time and space dependences...

Inspired by models for A+A→A(0) reactions with non-Brownian diffusion, we suggest a possible analytical explanation for the phenomena of anomalous coalescence of bubbles found in one-dimension (1d) by Josserand and Rica through numerical work [Phys. Rev. Letters 78 (1997) 1215]. The...

Negative differential conductivity in superlattices leads to the growth of inevitable spatial fluctuations. The spatially homogeneous electron distribution then becomes unstable, and a propagating electron accumulation-layer domain is formed. It is shown that envelopes of the wave functions are...

New exact solutions for the higher-order nonlinear Schrödinger equation and coupled higher-order nonlinear Schrödinger equations are obtained by using the generalized Jacobi elliptic function method. Solutions in the limiting cases are also studied.

In this paper we generalize a canonical model, recently proposed by us [Phys. Rew. E 58 (1998) 5574 and Phys. A 255 (1998) 474], describing a quantum system of particles obeying to a exclusion–inclusion principle. In the new model the system is coupled in a minimal fashion with an Abelian...

We investigate the dynamics of alpha-helical proteins with dipole and quadrupole type molecular excitations. Performing the symbolic computation on the iterative algorithm of Darboux transformation, we present the multisoliton solutions for the resulting fourth order nonlinear Schrödinger (NLS)...