Solitons are remarkable examples of coherent structures that emerge from the collective dynamics of nonlinear spatial systems. In this talk, we will use solitons as a guiding paradigm to explore the physics of emergence in spatially extended systems. We will first introduce how the balance between nonlinearity and dispersion produces conservative solitons, and then turn to dissipative solitons, which arise in systems maintained far from thermodynamic equilibrium and behave as dynamical attractors. We will examine how localized structures emerge through pattern-forming instabilities, bistability, and front interactions, and how their bifurcations can lead to stationary and oscillatory states, excitability, and complex spatiotemporal behavior.
The final part will explore conservative solitons in nonlinear field theories and their particle-like dynamics, including the emergence of mass, momentum, and effective Newtonian motion from the field equations. We will then discuss how an ensemble of such solitons moving on a fluctuating background can give rise, at the statistical level, to dynamics described by the Schrödinger equation.
The talk will move from waves to localized structures, from self-organization to dynamics, and finally from fields to particles, using solitons to illustrate a central theme of complex-systems physics: how qualitatively new physical entities and laws can emerge from the collective dynamics of nonlinear spatial systems.
Coffee and cookies will be served 15 minutes before the start of the seminar
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