# Simulating and Visualizing Complex Nonlinear PDEs-6/12

> 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 ](https://viadean.notion.site/Simulating-and-Visualizing-Complex-Nonlinear-PDEs-From-KdV-to-Geometric-Problems-in-the-Cloud-21d1ae7b9a3280be854ccdee07f5fc52?source=copy_link)like the KdV equation, and facilitates the setup and visualization for advanced mathematical problems such as optimal transport and prescribing Gaussian curvature.

### :clapper:Animated result

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Soliton propagation
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{% embed url="<https://youtu.be/l2RcEIIiAhs>" %}
Multi-Soliton Interaction
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