The soliton solution of the integrable coupled nonlinear Schrödinger equation (NLS) of Manakov type is investigated by using Zakharov-Shabat (ZS) scheme. We get the bright N-solitons solution by solving the integrable uncoupled NLS of Manakov type. We also find that there is an elastic collision of the bright N-solitons. [email protected] [email protected] 1

The propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear Schrrdinger equation (NLS). When considering realistic fibers one must examine perturbed NLS equations, with the particular perturbation depending on the physical situation that is being modeled. A common example is the complex Ginzburg-Landau equation (CGL), which is a dissipative perturbation...

In this paper, rogue wave solutions of a sixth-order focusing nonlinear Schrödinger (NLS) equation with variable coefficients are investigated on periodic background. To get the results, we take advantage Darboux transformation approach and nonlinearization spectral problem firstly find one kind solution that evolves periodically time spatial Besides, also dissipates over time. Modulation insta...

We study the instability of algebraic solitons for integrable nonlinear equations in one spatial dimension that include modified KdV, focusing NLS, derivative NLS, and massive Thirring equations. We develop the analysis of the Evans function that defines eigenvalues in the corresponding Lax operators with algebraically decaying potentials. The standard Evans function generically has singulariti...

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neuralnetwork learning to a linear quantum Schrödinger equation, as a result we get a nonlinear Schrödinger equation (NLS), performing as a quantum stochastic filter. In this paper, we present a bidirectional quantum associative memory model f...

Many equations can be expressed as a cubic nonlinear Schrödinger (NLS) equation with additional terms, such as the Davey-Stewartson (DS) system [1]. As it is the case for the NLS equation, the solutions of the DS system are invariant under the pseudo-conformal transformation. For the elliptic NLS, this invariance plays a key role in understanding the blow-up profile of solutions, whereas in the...

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasione-dimensional azimuthal equation of motion, and then applying a stability analysis in Fo...

Attractivity of the Ginz-burg-Landau mode distribution for a pattern forming system with marginally stable long modes. Justification of the 2D NLS equation – Quadratic resonances do not matter in case of analytic initial conditions. Justification of the Nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. approximation of time osc...