Postgraduate Thesis uoadl:1319002 181 Read counter

Κατεύθυνση Εφαρμοσμένα Μαθηματικά

Library of the School of Science

Library of the School of Science

2016-09-22

2016

Καλότυχου Δανάη

Ιωάννης Στρατής Καθηγητής (επιβλέπων), Δημήτριος Φραντζεσκάκης Καθηγητής, Νικόλαος Καραχάλιος Καθηγητής

Μη γραμμικές κυματικές εξισώσεις με διασπορά

Greek

Nonlinear dispersive wave equations

This thesis has as main object to study water wave equations and their

connection with extreme phenomena of the sea, such as tsunamis, rogue waves and

super rogue waves.

Initially, we mention the fundamental equations of continuity, momentum and

pressure, and also the framework of Euler equation in order to introduce the

linear wave equations.

Afterwards, we focus on the theory of shallow water. Here we discuss solitary

waves, called solitons. Naval architect J. S. Russell, through experiments

found, inter alia, that the wave speed depends on the height and thus concluded

that there must be a nonlinear effect. J. Boussinesq, D. Korteweg and G. de

Vries produced approximate nonlinear equations for shallow water waves and also

individual and periodic solutions of nonlinear wave equations for them

mentioned above. They also found that the wave speed is proportional to

amplitude, i.e. longer waves travel faster. Kadomtsev and Petviashvili included

in their equations weak transverse variation and so dispersion was connected.

The inverse rate of the increase of the amplitude of the linear shallow water

wave approaching a shore and gentle slope is given by the Bessel equation and

quantified by Green's lαw.

Then we will discuss the production of Nonlinear Schrodinger (NLS) equation in

the theory of shallow and deep waters and the relationship with solitons, as

well. In addition, we will refer to multidimensional water waves and the

equations generated not only without the influence of surface tension but also

under it.

connection with extreme phenomena of the sea, such as tsunamis, rogue waves and

super rogue waves.

Initially, we mention the fundamental equations of continuity, momentum and

pressure, and also the framework of Euler equation in order to introduce the

linear wave equations.

Afterwards, we focus on the theory of shallow water. Here we discuss solitary

waves, called solitons. Naval architect J. S. Russell, through experiments

found, inter alia, that the wave speed depends on the height and thus concluded

that there must be a nonlinear effect. J. Boussinesq, D. Korteweg and G. de

Vries produced approximate nonlinear equations for shallow water waves and also

individual and periodic solutions of nonlinear wave equations for them

mentioned above. They also found that the wave speed is proportional to

amplitude, i.e. longer waves travel faster. Kadomtsev and Petviashvili included

in their equations weak transverse variation and so dispersion was connected.

The inverse rate of the increase of the amplitude of the linear shallow water

wave approaching a shore and gentle slope is given by the Bessel equation and

quantified by Green's lαw.

Then we will discuss the production of Nonlinear Schrodinger (NLS) equation in

the theory of shallow and deep waters and the relationship with solitons, as

well. In addition, we will refer to multidimensional water waves and the

equations generated not only without the influence of surface tension but also

under it.

Wave, Tsunamis, Water wave equations, Rogue wave, Shallow water

No

0

Yes

22

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