Investigations On The Solutions And Transmission Property Of Solitary Wave In Nonlocal Nonlinear Media

The nonlinear optics gradually develops into an emerging discipline with the emergence of laser technology and has made remarkable achievements in recent years, nonlinear science has greatly promoted the development of science and technology and has raised the research interests about the related branch research of nonlinear optics. Many physical problems and phenomena in nonlinear science eventually comes down to the problem of solving the nonlinear Schrodinger equation, thus it is important to solving all kinds of nonlinear Schrodinger equations. In this paper, the analytical solutions of several kinds of nonlinear Schrodinger equations in the nonlinear media are solved, we obtain some characteristics and laws when the solitary waves transmit in the nonlinear media. The contents and achievements are as follows:1. We give a research for the analytical solution of nonlinear equations under the modulation of a two-dimensional or three-dimensional harmonic oscillator potential in strongly nonlocal nonlinear medium.The solutions of solitary waves under two-dimensional or three-dimensional harmonic oscillator modulation are investigated by self-similar technique, and the transmission properties of solitary waves are discussed by numerical simulation. It is found that under two-dimensional harmonic oscillator modulation the solution of solitary waves is Hermite Polynomial, which are similar to the bright solitons which the energy is biggest in the middle of the wave packet and form matrix wave packets in geometry. The total number and distribution form of wave packets, which are a matrix or a square matrix, are both influenced by the quantum number of x, y direction. The amplitude of wave packets energy increases gradually along the positive and negative direction of xy axis, and the energy of wave packets of matrices is diagonal symmetrical or xy axis symmetrical. That is to say, under the harmonic oscillator potential modulation, nonlinear system can show the character of stable Hermite solitary wave. These results have guiding significance for further study of the fidelity, loss, collapse and transmission properties of bright and dark solitons under two-dimensional, three-dimensional harmonic oscillator and other forms modulations of potential.2. The three-dimensional Hermite-Bessel-Gaussian spatial soliton clusters in strongly nonlocal nonlinearity media are studied.We demonstrate the existence of the Hermite-Bessel-Gaussian spatial soliton clusters in three-dimensional strongly nonlocal media by self-similar technique, both analytically and numerically. It is found that the soliton clusters display the vortex, dipole azimuthon and quadrupole azimuthon in geometry and the total number of solitons in the necklaces depends on the quantum number n and m of the Hermite functions and generalized Bessel polynomials. The numerical simulation is basically identical with the analytical solution, and the white noise does not lead to collapse of the soliton, which confirms the stability of the soliton waves. The theoretical predictions may give new insights into low-energetic spatial soliton transmission with high fidelity.3. The analytical solutions and the soliton solutions of one-dimensional generalized inhomogeneous nonlinear Schrodinger equations with various external potentials are studied.A class of analytical traveling wave and soliton solutions to the generalized inhomogeneous nonlinear Schrodinger equation with some typical external potentials is constructed by using the balance principle and the F-expansion technique. New constraint conditions on the equation for analytical solutions are found at the same time, which admit different types of external potentials. Several analytical traveling wave and soliton solutions, which have important applications of physics, and their integrability conditions with some typical external potentials are studied in details. The stability analysis of the solutions is discussed numerically, the results show that stable propagation of solitons can be maintained in the nonuniform distributed nonlinear media.4. The analytical solutions and the soliton solutions of one-dimensional nonlinear Schrodinger equations with nonparaxial item are studied.The one-dimensional nonlinear Schrodinger equations with nonparaxial item in nonlinear media are solved by the balance principle and F development technology, we obtain four periodic travelling wave solutions with different initial and constraint condition; Then, take the first case for instance, we discussed that the periodic travelling wave solutions are degenerated into soliton solutions and the constraint condition is obtained when the mode parameter m approaches to be1; Finally, we carry on the numerical analysis by choosing several groups of soliton solution of the first case, we obtain the conclusion that these soliton solutions are stable, thus, we still can obtain stable soliton solution through choosing appropriate modulation parameters even the nonparaxial modulation is contained.