Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters

Non-diffracting multi-electron vortex beams balancing their electron–electron interactions

“…This means that, while the nonlinear non-diffracting wavepackets in the Newton–Schrödinger model are solitons, and are therefore localized and square-integrable 41 , we expect the localized non-diffracting solutions of Eqs ( 6 ) and ( 7 ) to be not square-integrable. Intuitively, seeking localized solutions for Eqs ( 6 ) and ( 7 ) resembles searching for non-diffracting beams in self-defocusing thermal optical nonlinearities, which fundamentally cannot support bright solitons but can support dark solitons 45 and also localized non-diffracting wavepackets that are not square integrable (e.g., nonlinear Bessel-like beams 46 ).…”

“…Intuitively, seeking localized solutions for Eqs. 5 resembles searching for non-diffracting beams in self-defocusing thermal optical nonlinearities, which fundamentally cannot support bright solitons but can support dark solitons 38 and also localized non-diffracting wavepackets that are not square integrable (e.g., nonlinear Bessel-like beams 39 ).…”

Breathing Azimuthons in Nonlocal Nonlinear Media

“…In [10], author discussed (6) with β (z) = s(z) = 1, g(z) = 0, and gain the rotating azimuthon, which can be reduced to the radially symmetric optical vortex soliton under certain conditions. Further on, [12] investigated (6) with space-dependent diffractive and gain coefficient for the first time and gain the non-rotating Bessel solitary wave. We introduce a set of self-similar transformation as follows: …”

“…These higher-order solitons are obtained as a generalization of the Whittaker linear modes in the case of the Gaussian response function. Reference [12] studied Bessel solitary wave (BSW) solutions to a twodimensional strongly nonlocal nonlinear Schrodinger equation with distributed coefficients and compared the features of BSW with that of Hermite solitary waves and Laguerre solitary waves. Recently, a variety of dynamics both for vortex-vortex and vortexantivortex pairs in nonlocal nonlinear media have been demonstrated in [13].…”

Self-similar solitary wave family in Bessel lattice

“…24,25 Higher-dimensional solitary waves may analogously experience varying diffraction, nonlinearity, and gain. [26][27][28] First, diffractive coefficient is β = 1 2k 0 n 0 , so the diffractive property is related with wavelength (λ = 2π k 0 ) and linear refractive index n 0 besides the width of the beam, and thus β varies along with propagation distance z if n 0 is a function of z. Second, any real material experiences parameter perturbation due to the inhomogeneous material and the fluctuation of environment temperature, etc.…”