2 citations · 3 across the 10 of their papers we have counts for
7 papers · 1 filter
A tale of two Nekrasov's integral equations
Nikolay Kuznetsov
Just 100 years ago, Nekrasov published the widely cited paper \cite{N1}, in which he derived the first of his two integral equations describing steady periodic waves on the free su…
The floating-body problem: an integro-differential equation without irregular frequencies
Nikolay Kuznetsov
The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstac…
Modified Babenko's equation for periodic gravity waves on water of finite depth
Evgueni Dinvay, Nikolay Kuznetsov
A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko's equation considered in \cite{KD}. Both operat…
On the absence of trapped water waves near a cliffed cape
Nikolay Kuznetsov
The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is suppo…
A Faber--Krahn inequality for indented and cut membranes
Nikolay Kuznetsov
In 1960, Payne and Weinberger proved that among all domains that lie within a wedge (an angle whose measure is less than or equal to ), and have a given value of a certain integ…
Two-dimensional water waves in the presence of a freely floating body: conditions for the absence of trapped modes
Nikolay Kuznetsov
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth int…