Real-time dynamics of optical controlling for bound states of mode-locked fiber laser with short-range interaction

Novel constructed dark, bright, and rogue waves of three models of the well-known nonlinear Schrödinger equation

“…In this section, we'll have a look at the various physical interpretations of the previously-proposed fixes. A number of different diagrams (1,2,3,4) have been used to illustrate the Eqs. ( 5), (30), (57), respectively.…”

“…Using these diagrams, you can see how mass location and time dependence affect the kinetic energy operator's nature and how it may be represented in polar, contour, two-dimensional, and threedimensional graphs. Illustrations (1,2,3,4) show brilliant, dark, and periodic soliton waves in various graph types.…”

“…Nonlinear partial differential equations (PDEs) are frequently utilized in a variety of sectors of study, most notably physics, to explain complicated processes [1,2,3]. As a result, tackling nonlinear issues is critical in nonlinear sciences [4,5].…”

Dissipative soliton breathing dynamics driven by desynchronization of orthogonal polarization states

“…5,20,21 The strong, short-range interactions lead to the narrow spacing of the few pulse widths and locked phase differences between adjacent solitons, resulting in the highly challenging realtime characterization of their detailed temporal structure. 5,20,21 Long-range interactions can be driven by Casimir-like, 19,25 optoacoustic 17,18,20,24 polarization instabilities, [13][14][15][16] and solitondispersive wave interaction, [6][7][8][9][10][11][12]31 leading to the formation of the soliton structures in the form of multi-pulsing, harmonic mode locking, soliton rain, rogue waves, and breathers. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]24,25,31 Breathing solitons, known as dynamic DSs, typically feature profile and energy oscillation (breath) of DSs with periods from 5 to 100 round trips (RTs).…”

“… – 4 However, in the practical context, targeting the collective patterns under demand is challenging due to the limited ability to conduct experiments on manipulating engineering and biological networks’ structure 1 – 4 The short pulse duration of hundreds of femtoseconds and repetition rates of tens of hundreds of megahertz make mode-locked lasers (MLLs) suitable testbeds for studying the synchronization-driven self-organization in the form of dissipative solitons (DSs)—ubiquitous localized wave packets arising from the balance between dissipative and dispersive effects 5 – 27 For example, recently demonstrated orthogonal states of polarization (SOPs) of DSs show a resemblance of coupled oscillators with various synchronization behaviors 15 , 28 …”