Peregrine Solitons on a Periodic Background in the Vector Cubic-Quintic Nonlinear Schrödinger Equation

Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

“…Thus the methodology and results presented in this manuscript serve the required purposes and they will be helpful for characterising the dynamical behaviour of nonlinear waves on different backgrounds. Particularly, the present route of extracting nonlinear wave solutions has an extra advantage over Darboux transformation and other methods for NLS, KdV, sG, Hirota and their coupled family of equations [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], in terms of reducing the mathematical/computational complexity as well as a richer variety of solution profiles. To be precise, we have utilized simple exponential and polynomial type test functions as initial seed solutions to obtain the kink soliton (7) and rogue wave (10d), respectively, which manifested themself to produce various wave phenomena due to the available arbitrary backgrounds (8).…”

“…Particularly, the physical motivation to look for such nonlinear waves on non-uniform/varying backgrounds starts from the situation of randomly varying surface or deep water waves to inhomogeneous plasma, layered magnetic materials, inhomogeneous optical media, and atomic condensate system [22][23][24][25]. As a result of this search, some localized nonlinear waves on varying backgrounds are investigated in recent times, which include the rogue waves on cnoidal, periodic, and solitary wave backgrounds in one-dimensional models such as focusing NLS model [26][27][28][29], derivative NLS equation [30][31][32], higher-order nonlinear Schrödinger equation [33,34], higher-order modified KdV equation [35], modified KdV models [36,37], Hirota equation [38,39], Gerdjikov-Ivanov model [40], sine-Gordon equation [41,42], Fokas model [43], and coupled cubic-quintic NLS equation [44] as well as vector Chen-Lee-Liu NLS model [45]. Mostly, the method used in these studies is nothing but the Darboux transformation which requires Lax pair and involves complex mathematical calculations.…”

Approaching Electroencephalographic Pathological Spikes in Terms of Solitons

“…Due to a delicate balance between dissipative effects and nonlinear dynamics, solitons are coherent structures propagating in space and time at a constant velocity without attenuation, distortion, or energy loss [2,3]. At least in an idealized framework, the stability and stationarity of soliton's analytical solutions are confirmed against non-integrable perturbations [4] (Ye et al, 2020) so that frictional effects like viscosity do not cause solitons to decay over time [5]. The energy of solitons is carried adiabatically through the medium, i.e., without transferring heat or mass [6].…”

Soliton Interactions with Different Dispersion Curve Functions in Heterogeneous Systems

“…[9][10][11][12] On the one hand, soliton theory in integrable systems plays an important role in some fields. [13][14][15] For example, in fiber optic communication, solitons are widely used due to their advantages such as large capacity, low bit error rate, and long-distance transmission. [16] Solitons are used to address the dispersion effects of light propagation in fiber optic communication systems.…”