Abstract

The one-dimensional suspension bridge equation has been well studied: traveling waves of various types have been proven to exist. Far less is known about the two-dimensional case. We use computer-assisted proof methods to find and prove periodic traveling waves in two spatial dimensions, ensuring rigorous control over computational errors.

Additionally, we extend computer-assisted proof techniques from existing literature on two-dimensional periodic solutions in the forced Navier-Stokes equations to three dimensions to prove traveling wave solutions. Challenges posed by the higher-dimensional nature of the problem are alleviated by employing symmetry arguments.

 

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