In this paper, a high-order method for solving the Schrodinger equation is introduced. We apply a compact finite difference approximation for discretizing spatial derivatives and we use the C-cubic spline collocation method for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. W...

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This integrable and admits Lax pair. The LPD generalization of nonlinear Schrodinger (NLS) described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using sine-cosine method hyperbolic tangent a variety new exact solutions are obtained. These methods effective tools for searching partial differential equations in mathemat...

In Section 1 we present a general principle for associating nonlinear equations of evolutions with linear operators so that the eigenvalues of the linear operator are integrals of the nonlinear equation. A striking instance of such a procedure is the discovery by Gardner, Miura and Kruskal that the eigenvalues of the Schrodinger operator are integrals of the Korteweg-de Vries equation. In Secti...

A simulation formalism for the nonlinear response of vibrational excitons is presented and applied to the OH stretching vibrations of neat liquid H(2)O. The method employs numerical integration of the Schrodinger equation and allows explicit treatment of fluctuating transition frequencies, vibrational couplings, dipole moments, and the anharmonicities of all these quantities, as well as nonadia...

The problem of modulation instability of a self-focused beam in a homogeneous nonlinear medium with saturation and anomalous group-velocity dispersion is solved numerically. It is shown that the results of this instability is beam breakup into a periodic train of three-dimensional (3D) spatial solitary waves. It is also shown that other types of periodic initial conditions can produce a periodi...

We study the performance of a typical fiber-optic communication link operating at 10 Gbps, comprising of multiple spans of standard single mode fiber (SSMF), in-line amplifiers and dispersion compensating fibers (DCF). The effects of attenuation, chromatic dispersion, nonlinearity and polarization mode dispersion (PMD) are taken into account. By numerically solving the non-linear Schrodinger eq...

A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on coupled nonlinear Schr\"odinger equation in birefringent fibers. At same time, elastic collision process mixed bright-dark soliton predicted. Compared predicted results with exact solution, method proven be effective solve equation. Moreover, d...