Optical solitons for paraxial wave equation in Kerr media

This paper retrieves Jacobi elliptic, periodic, bright and singular solitons for paraxial nonlinear Schrödinger equation (NLSE) in Kerr media. We use extended trial equation method to obtain these solitons solutions. For the existence of the soliton solutions, constraint conditions are also presented.

Смещенные параксиальные пучки Бесселя--Гаусса. I

We have considered a new family of localized solutions of a parabolic (paraxial wave) equation that generalizes the well-known Bessel–Gaussian beams and includes asymmetric and noncoaxial Bessel–Gaussian beams as subfamilies. The Fourier spectra of these solutions have been found, and their expansions into nonshifted Bessel–Gaussian beams have been obtained.