Dresden 2026 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 22: Pattern Formation
DY 22.2: Vortrag
Dienstag, 10. März 2026, 09:45–10:00, ZEU/0118
Dynamics of localized states in a weakly dissipative Korteweg-de Vries-Kuramoto-Sivashinsky Equation — •Justus Keußen1, Daniel Greve1, Julien Javaloyes2, and Svetlana V. Gurevich1,2,3 — 1Institute for Theoretical Physics, University of Münster, Münster, Germany — 2Universitat de les Illes Balears, Palma, Spain — 3Center for Data Science, University of Münster, Münster, Germany
We are interested in the dynamics of localized solutions in a weakly dissipative Korteweg de Vries Kuramoto Sivashinsky equation, using a combination of analytical, numerical, and path-continuation methods. We show that a traveling solitary soliton exists and is stable over a certain parameter range, even though the homogeneous state is linearly unstable. Furthermore, we employ a variational ansatz to analytically determine the selected velocity of the localized state. Finally, path continuation in the domain size reveals that the corresponding bifurcation points on both the homogeneous and solitary branches follow a power-law scaling with the system length, implying that each domain size admits a finite interval of parameter values in which a stable solitary wave exists.
Keywords: dissipative solitons; numerical continuation; bifurcation analysis; solitons on unstable background; conservation law