Exact spatial soliton solutions of the two-dimensional generalized nonlinear Schrödinger equation with distributed coefficients

Hollow ring-like soliton and dipole soliton in ( $$\varvec{2+1}$$ 2 + 1 )-dimensional $$\varvec{\mathcal {PT}}$$ PT -symmetric nonlinear couplers with gain and loss

“…In order to obtain fundamental soliton solutions, we expand functions g(r, z) and f (r, z) as power series of a formal expansion parameter , and truncate g(r, z) as g(r, z) = g 1 (r, z) and f (r, z) as f (r, z) = 1 + 2 f 2 (r, z) [25]. Inserting these expressions into Eqs.…”

“…where parameter q ∈ [0, 1] determines the modulation depth of the beam, and the topological charge m ≥ 0 is an integer [25]. Note that solution (5) is an approximate solution of Eq.…”

“…According to the Hirota bilinear method [25], inserting U = r g(r,z) f (r,z) with the complex and real functions g(r, z) and f (r, z) into Eq. (6), we have…”

Stable 2D localized modes in anisotropic media with harmonic and PT-symmetric potentials

“…Zhong et al. [22] gave exact spatial soliton solutions for the (2 + 1) D NLSE by the F-expansion technique with the assumption of the ansatzs.…”

Breathing Azimuthons in Nonlocal Nonlinear Media

“…And there are many novel features of the nonlocal nonlinearity for the evolution of waves, such as vortex solitons, Gaussian solitons, soliton cluster, ellipticons, and the rotating nonlinear wave solutions, the so called azimuthons. Some of them are as follows: In [11], the existence and the stability of Whittaker solitons have been introduced and analyzed numerically. These higher-order solitons are obtained as a generalization of the Whittaker linear modes in the case of the Gaussian response function.…”