Hermite-Gaussian Vector soliton in strong nonlocal media

Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformation

“…Following our earlier works [15] in the literature, a family of analytical solutions termed breathers (pulsating modes) can typically be obtained through an expansion scheme (ζ (1) , ζ (2) being arbitrary complex phase factors):…”

“…The constraint 2σρ 2 > p 2 must hold for Ω to be real and M > 1. The breather can also be expressed in terms of hyperbolic and trigonometric functions as (g 1 complex, f 1 real and as illustrative example here ζ (1) = ζ (2) = ζ (real))…”

“…To generate the rogue waves, a long wave limit (p tending to zero) is now taken with the provision exp(ζ (1) ) = exp(ζ (2) ) = -1.…”

“…Such equations have been studied frequently in applied disciplines, e.g. spatiotemporal solitary waves [1] and Hermite-Gaussian beams [2] are considered in nonlocal optical media.…”

Propagation Property of an Astigmatic sin–Gaussian Beam in a Strongly Nonlocal Nonlinear Media

“…Distinct from the conventional local nonlinearity, the nonlocality allows the refractive index of the media at a particular point to be related to the beam intensity at all other points. Note that the nonlocal nonlinearity which can support a variety of nonlocal spatial optical solitons exhibits in many physical systems, and some of them have been observed experimentally [3][4][5][6][7][8][9][10]. Moreover, it has been reported that a great number of optical beams can steadily propagate in SNNM under sufficient conditions, including Gaussian beams and higher-order Gaussian beams, four-petal Gaussian beams, Lorentz-Gaussian beams, the beams carrying wave front dislocations such as Hermite-, Hermite-cosh-or Laguerre-Gaussian beams, and so on [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”