most citedOn completely integrable polynomial PDEs arising from Sturm-Liouville differential equation using evolutionary vessels. KdV Hierarchy

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math-ph2012★ 1 cited

Solution of the Sturm-Liouville and the Korteweg-de-Vries equations with periodic and quasi-periodic parameters using theory of vessels

Andrey Melnikov

We prove the existence of solutions to the Sturm-Liouville (SL) equation -y"(x)+q(x)y(x) = s^2 y(x) with periodic and quasi-periodic potential q(x) using theory of SL vessels, impl…