Soliton-like behaviour in multi-component Nonlinear Schrödinger equations
Nonlinear Schrodinger (NLS) Equation is ubiquitous in physics, still not much is known about the dynamics of the equation. Through our investigation, we found that multicomponent NLS system can be mapped to an uncoupled Korteweg-de Vries (KdV) system. Since KdV is an integrable system we can know about certain qualitative aspects of multicomponent NLS from this mapping. One interesting feature of KdV equation is that it has a special solution called solitons, these special profiles balance the nonlinear and the dispersive effects in the system to give traveling wave packets. Leveraging our mapping one can find similar solutions for multicomponent NLS systems as well.