Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)

We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) . The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal reverse-space, reverse-time and reverse-spacetime nonlinear Schrödinger equations associated with so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) .

Collapse arrest for two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam in nonlocal nonlinear media

Propagation dynamics of two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam are investigated numerically in local and nonlocal nonlinear media. The self-healing and collapse of the beam depend crucially on the distribution factor $b$ and the topological charge $m$. With the help of nonlocality, stable Airy Gaussian beam and Airy Gaussian vortex beam with larger amplitude can be obtained, which always collapse in local nonlinear media. When the distribution factor $b$ is large enough, the Airy Gaussian vortex beam will transfer into quasi-vortex solitons in nonlocal nonlinear media.

The Soliton Solutions and Long-Time Asymptotic Analysis for an Integrable Variable Coefficient Nonlocal Nonlinear Schrödinger Equation

An integrable variable coefficient nonlocal nonlinear Schrödinger equation (NNLS) is studied; by employing the Hirota’s bilinear method, the bilinear form is obtained, and the N -soliton solutions are constructed. In addition, some singular solutions and period solutions of the addressed equation with specific coefficients are shown. Finally, under certain conditions, the asymptotic behavior of the two-soliton solution is analyzed to prove that the collision of the two-soliton is elastic.