Chaos control in the nonlinear Schrdinger equation with Kerr law nonlinearity

The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.

Solving coupled nonlinear Schrodinger equations via a direct discontinuous Galerkin method

In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.

A TWO-GRID FINITE-ELEMENT METHOD FOR THE NONLINEAR SCHRODINGER EQUATION

In this paper, some two-grid finite element schemes are constructed for solving the nonlinear SchrSdinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy.

A numerical study of the generation mechanism of internal solitary waves in the Luzon Strait

The South China Sea （SCS） is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in the Luzon Strait. The generation mechanism of the internal solitary waves in the Luzon Strait is discussed using a modulation instability. The energy gain of the modulation instability is derived based on the fully nonlinear Schr6dinger equation. The peak value of the gain is calculated under different conditions of stratification, wavelength and the initial amplitude of an internal tidal wave. The characteristics of the modulation instability in the Luzon Strait are investigated. The conditions that make the internal tidal wave evolve into an internal solitary wave in the Luzon strait are also obtained. The results show that the internal tide waves can generate the modulation instability in the Luzon Strait and that the maximum gain occur at the eastern sill of the Luzon Strait, where the internal tide waves start to break up into internal solitary trains. The magnitude and the scope of the peak gain are relevant to the stratification and the initial conditions of the internal tide waves. The numerical simulation results are consistent with the in-situ data.