102 research outputs found
A plethora of generalised solitary gravity-capillary water waves
The present study describes, first, an efficient algorithm for computing
capillary-gravity solitary waves solutions of the irrotational Euler equations
with a free surface and, second, provides numerical evidences of the existence
of an infinite number of generalised solitary waves (solitary waves with
undamped oscillatory wings). Using conformal mapping, the unknown fluid domain,
which is to be determined, is mapped into a uniform strip of the complex plane.
In the transformed domain, a Babenko-like equation is then derived and solved
numerically.Comment: 20 pages, 7 figures, 45 references. Other author's papers can be
downloaded at http://www.denys-dutykh.com
Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
The aim of this paper is the accurate numerical study of the KP equation. In
particular we are concerned with the small dispersion limit of this model,
where no comprehensive analytical description exists so far. To this end we
first study a similar highly oscillatory regime for asymptotically small
solutions, which can be described via the Davey-Stewartson system. In a second
step we investigate numerically the small dispersion limit of the KP model in
the case of large amplitudes. Similarities and differences to the much better
studied Korteweg-de Vries situation are discussed as well as the dependence of
the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at
http://www.mis.mpg.de/preprints/index.html
Nonlinear interaction of long-wave distrubances with short-scale oscillations in stratified flows
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1996.Includes bibliographical references (leaves 145-150).by Tian-Shiang Yang.Ph.D
On asymptotically equivalent shallow water wave equations
The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at
linear order in the asymptotic expansion for unidirectional shallow water
waves. However, at quadratic order, this asymptotic expansion produces an
entire {\it family} of shallow water wave equations that are asymptotically
equivalent to each other, under a group of nonlinear, nonlocal, normal-form
transformations introduced by Kodama in combination with the application of the
Helmholtz-operator. These Kodama-Helmholtz transformations are used to present
connections between shallow water waves, the integrable 5th-order Korteweg-de
Vries equation, and a generalization of the Camassa-Holm (CH) equation that
contains an additional integrable case. The dispersion relation of the full
water wave problem and any equation in this family agree to 5th order. The
travelling wave solutions of the CH equation are shown to agree to 5th order
with the exact solution
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