Research Projects

Soliton molecules (SMs) are bound states of two or more fundamental optical solitons that co-propagate with equal group velocities. A stable SM forms when its constituent solitons are at a specific equilibrium distance, where the net force between them is zero and the binding energy is minimum. Mathematically, bound states are represented by bound soliton state solutions, which are special cases of multi-soliton solutions of integrable nonlinear evolution equations under a specific choice of soliton velocities. The simplest bound state can be constructed from the two-soliton solution when the solitons propagate with identical velocities. Higher-order SMs arise from multifold velocity degeneracy, forming triplet and quadruplet states, as well as macromolecular states or soliton complexes composed of an arbitrary number of solitons. Recently, rapid progress has been made in understanding this novel soliton state since its experimental realization in dispersion-managed system along with identification of its internal dynamics, such as synthesis and vibration, akin to diatomic molecules in chemistry. These results help to explore how closely photonic SMs can behave like real matter molecules, even though they are very different in nature. Further, SMs also exhibit rich dynamics, including collision induced synthesis, dissociation, isomer formation, and polymerization into macromolecules and soliton crystals. Efforts have also been made to realize multicolor SMs, soliton molecular complexes, breather molecular states, supramolecular structures, and Hopf bifurcation-induced oscillations. From an application perspective, SMs have been proposed as ideal candidates for enhancing fiber data carrying capacity by offering extra bits for information encoding in optical telecommunications. However, much less effort has been taken to find the binding energy and interaction forces in terms of separation and relative phases of solitons while studying the scattering dynamics of SMs under external potentials and impurities. Additionally the control of SMs through dispersion/diffraction management as well as their robustness against perturbations remains less explored. Also, collision dynamics of SMs with solitons or with other SMs remain largely unexplored since soliton-soliton interactions are often considered detrimental to data transmission in fibers. Moreover, most studies focus on doublet and triplet SMs, which are composed of two and three solitons, respectively. Motivated by these, we aim to investigate the dynamics of SMs, their isomer structures and formation mechanisms. We also intend to explore their classification, stability against perturbations, transport properties under external potentials, and collision properties. These investigations will be carried out within nonlinear Schrödinger type models since these equations play a decisive role in governing the evolution of SMs. We would also like to extend this study to Heisenberg spin systems.

Nonlinear Schrödinger Equation, Solitons, Soliton molecules, Soliton molecular complexes, Integrable Systems, Non-integrable models