Nonlinear waves

Nonlinear waves are disturbances in a medium where the wave's behavior is influenced by its own amplitude, causing it to change shape or speed as it travels. Unlike linear waves, which maintain consistent form, nonlinear waves can become sharper, form patterns, or interact in complex ways. Examples include rogue waves in the ocean or shock waves in air, where the wave’s properties depend on its energy. These phenomena occur when the system’s responses aren’t directly proportional to the input, leading to rich and sometimes unpredictable behaviors in various natural and engineered systems.