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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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Are there soliton solutions for Euler and Navier–Stokes equation?
Yes!
There exist soliton solutions for the Navier Stokes d.e. (and thus also for the Euler d.e), these has been recently found.
Please look at the following citation;
r. meulens, "A note on N-soliton …