Sech-type and Gaussian-type light bullet solutions to the generalized (3 $$+$$ + 1)-dimensional cubic-quintic Schrödinger equation in $$\varvec{\mathcal {PT}}$$ PT -symmetric potentials

Diversity soliton excitations for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation

“…In the line with the development of symbolic computation, much work has been focused on the various extensions and application of the known algebraic methods to construct solutions of non-linear evolution equations [1][2][3][4]. Special solutions, such as dromions, soliton excitations, and other coherent structures, which might be useful in explaining some phenomena in both mathematics and physics, were discussed in open literature [5][6][7][8].…”

Controllable behaviors of Peregrine soliton with two peaks in a birefringent fiber with higher-order effects

“…and light bullet [7], exist in various nonlinear optical systems. As one of research focus, dynamical behaviors of rogue waves (RWs) [8] were intensively studied in different domains of physics, especially in fluid dynamics [9], nonlinear optical systems [10] and plasmas [11].…”

Spatiotemporal soliton structures in (3 $$+$$ + 1)-dimensional $$\mathcal {PT}$$ PT -symmetric nonlinear couplers with gain and loss

“…The pioneering theoretical research about the PT symmetry stimulates the study of soliton dynamics in PT -symmetric potentials in optics [24][25][26][27][28][29]. Stable two-dimensional (2D) localized spatial solitons in PT -symmetric potentials with power-law nonlinearity were discussed [24].…”

“…Gaussian-type light bullet solutions of the (3 + 1)-dimensional nonlinear Schrödinger equation with cubic and power-law nonlinearities in PT -symmetric potentials have been exhibited [26]. Sech-type and Gaussian-type light bullet solutions of the generalized (3 + 1)-dimensional cubic-quintic nonlinear Schrodinger equation in PTsymmetric potentials have been investigated, too [27]. Moreover, higher-dimensional solitons in PTsymmetric couplers have also been constructed [28,29].…”