🧠Simulating and Visualizing Complex Nonlinear PDEs-6/12

From KdV to Geometric Problems in the Cloud

The Korteweg-de Vries (KdV) equation, a fundamental nonlinear PDE, models diverse phenomena from shallow water waves and plasma physics to crystal lattices, serving as a cornerstone in integrable systems theory, soliton research via the inverse scattering transform, and connecting to quantum fluids, Hamiltonian systems, and forced oscillations.

Cloud computing enables the numerical simulation and dynamic visualization of complex nonlinear partial differential equations like the KdV equation, and facilitates the setup and visualization for advanced mathematical problems such as optimal transport and prescribing Gaussian curvature.

🎬Animated result

Soliton propagation

Multi-Soliton Interaction