Symmetries and casimir of an extended classical long wave system

Pramana ◽  
2013 ◽  
Vol 80 (4) ◽  
pp. 559-569 ◽  
Author(s):  
K M TAMIZHMANI ◽  
R ILANGOVANE ◽  
B DUBROVIN
Keyword(s):  
Wave System ◽  
Long Wave

Tsunamis

2009 ◽  
Author(s):  
Gerassimos Papadopoulos
Keyword(s):  
Large Scale ◽  
Aegean Sea ◽  
Volcanic Eruptions ◽  
Mediterranean Area ◽  
Wave System ◽  
Submarine Landslides ◽  
Plate Convergence ◽  
Long Wave ◽  
The Mediterranean ◽  
Steep Terrain

According to Imamura (1937: 123), the term tunami or tsunami is a combination of the Japanese word tu (meaning a port) and nami (a long wave), hence long wave in a harbour. He goes on to say that the meaning might also be defined as a seismic sea-wave since most tsunamis are produced by a sudden dip-slip motion along faults during major earthquakes. Other submarine or coastal phenomena, however, such as volcanic eruptions, landslides, and gas escapes, are also known to cause tsunamis. According to Van Dorn (1968), ‘tsunami’ is the Japanese name for the gravity wave system formed in the sea following any large-scale, short-duration disturbance of the free surface. Tsunamis fall under the general classification of long waves. The length of the waves is of the order of several tens or hundreds of kilometres and tsunamis usually consist of a series of waves that approach the coast with periods ranging from 5 to 90 minutes (Murty 1977). Some commonly used terms that describe tsunami wave propagation and inundation are illustrated in Figure 17.2. Because of the active lithospheric plate convergence, the Mediterranean area is geodynamically characterized by significant volcanism and high seismicity as discussed in Chapters 15 and 16 respectively. Furthermore, coastal and submarine landslides are quite frequent and this is partly in response to the steep terrain of much of the basin (Papadopoulos et al. 2007a). Tsunamis are among the most remarkable phenomena associated with earthquakes, volcanic eruptions, and landslides in the Mediterranean basin. Until recently, however, it was widely believed that tsunamis either did not occur in the Mediterranean Sea, or they were so rare that they did not pose a threat to coastal communities. Catastrophic tsunamis are more frequent on Pacific Ocean coasts where both local and transoceanic tsunamis have been documented (Soloviev 1970). In contrast, large tsunami recurrence in the Mediterranean is of the order of several decades and the memory of tsunamis is short-lived. Most people are only aware of the extreme Late Bronge Age tsunami that has been linked to the powerful eruption of Thera volcano in the south Aegean Sea (Marinatos 1939; Chapter 15).

Non-TravellingWave Solutions of the (2+1)-Dimensional Dispersive Long Wave System

2009 ◽  
Vol 64 (9-10) ◽  
pp. 540-552
Author(s):  
Mamdouh M. Hassan
Keyword(s):  
Expansion Method ◽  
Travelling Wave ◽  
Hyperbolic Function ◽  
Wave System ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Rational Solutions ◽  
Long Wave ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

With the aid of symbolic computation and the extended F-expansion method, we construct more general types of exact non-travelling wave solutions of the (2+1)-dimensional dispersive long wave system. These solutions include single and combined Jacobi elliptic function solutions, rational solutions, hyperbolic function solutions, and trigonometric function solutions.

scholarly journals Approximate solution of solitary wave for nonlinear-disturbed time delay long-wave system

2014 ◽  
Vol 63 (11) ◽  
pp. 110204
Author(s):  
Wang Wei-Gang ◽  
Lin Wan-Tao ◽  
Shi Lan-Fang ◽  
Mo Jia-Qi
Keyword(s):  
Approximate Solution ◽  
Time Delay ◽  
Solitary Wave ◽  
Wave System ◽  
Long Wave

Harbour resonance due to set-down beneath wave groups

1977 ◽  
Vol 79 (1) ◽  
pp. 71-92 ◽  
Author(s):  
E. C. Bowers
Keyword(s):  
Group Velocity ◽  
Wave System ◽  
Primary Wave ◽  
Natural Oscillations ◽  
Natural Period ◽  
Wave Groups ◽  
Long Period ◽  
Natural Modes ◽  
Long Wave ◽  
Harbour Resonance

Natural modes of water oscillation inside harbours are known to occur with periods of the order of minutes. It seems likely that these oscillations are excited by water fluctuations of similar period outside the harbour and an often quoted cause of such fluctuations is the phenomenon of surf beats. These are thought to be long waves which are reflected back out to sea when a primary wave system breaks upon a beach. In this paper it is shown theoretically that the natural oscillations of a harbour can be excited directly, without breaking of the primary wave system, by set-down beneath wave groups, which is a long-period disturbance travelling towards the shore line at the group velocity. This theory is in agreement with model experimental results which show that, when the group period is close to a natural period of the harbour, resonance will occur with the set-down behaving as if it were a real long wave.

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