Related papers: Interaction of pulses in nonlinear Schroedinger mo…
We study $n$-pulse interaction in fast collisions of $N$ solitons of the cubic nonlinear Schr\"odinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a reduced model that yields the contribution of $n$-pulse…
The interaction between two co-propagating electromagnetic pulses in a magnetized plasma is considered, from first principles, relying on a fluid-Maxwell model. Two circularly polarized wavepackets by same group velocities are considered,…
We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation…
In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light…
A double pair plasma system containing cold inertial positive and negative ions, and inertialess super-thermal electrons and positrons is considered. The standard nonlinear Schr\"{o}dinger equation is derived by using the reductive…
The stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, is studied for the cases of a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight…
In quantum mechanics, collisions between two particles are captured by a scattering matrix which describes the transfer from an initial entrance state to an outgoing final state. Analyticity of the elements of this $S$-matrix enables their…
We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find…
We study the behavior of the soliton solutions of the equation i((\partial{\psi})/(\partialt))=-(1/(2m)){\Delta}{\psi}+(1/2)W_{{\epsilon}}'({\psi})+V(x){\psi} where W_{{\epsilon}}' is a suitable nonlinear term which is singular for…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
The perturbation theory based on the Riemann-Hilbert problem is developed for the modified nonlinear Schr{\"o}dinger equation which describes the propagation of femtosecond optical pulses in nonlinear single-mode optical fibers. A detailed…
In many contexts, the interaction between particles gives rise to emergent and perhaps unanticipated physical phenomena. An example is the fractional quantum Hall effect, where interaction between electrons gives rise to fractionally…
We investigate bright solitons in the one-dimensional Schr\"odinger equation in the framework of an extended variational approach. We apply the latter to the stationary ground state of the system as well as to coherent collisions between…
We investigate a propagation of solitons for nonlinear Schr\"odinger equation under small driving force. The driving force passes through the resonance. The process of scattering on the resonance leads to changing of number of solitons.…
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical…
Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged. The two solitons merge into one…
We investigate numerically by a conservative difference scheme in complex arithmetic the head-on and takeover collision dynamics of the solitary waves as solutions of linearly Coupled Nonlinear Schr\"odinger Equations for various initial…
The Boltzmann type kinetic equation for solitons in Nonlinear Schr\"{o}dinger equation has been constructed on the base of analysis of two soliton collision. Possible applications for Langmuir solitons in plasma and solitons in optic fiber…
We analytically study nonlinear quasi-monochromatic plasma waves in a two-dimensional electron system set between the two metal electrodes (gates). We derive a nonlinear Schrodinger equation for a slow-varying envelope to describe the…