Solitons, breathers and rational solutions for a (2+1)-dimensional dispersive long wave system

2022 ◽  
pp. 133140
Author(s):  
Han-Han Sheng ◽  
Guo-Fu Yu
2009 ◽  
Vol 64 (9-10) ◽  
pp. 540-552
Author(s):  
Mamdouh M. Hassan

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.


Author(s):  
Gerassimos Papadopoulos

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).


2020 ◽  
pp. 2150057
Author(s):  
Xin-Mei Zhou ◽  
Shou-Fu Tian ◽  
Ling-Di Zhang ◽  
Tian-Tian Zhang

In this work, we investigate the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko (gBK) equation. Based on its bilinear form, the [Formula: see text]th-order breather solutions of the gBK equation are successful given by taking appropriate parameters. Furthermore, the [Formula: see text]th-order lump solutions of the gBK equation are obtained via the long-wave limit method. In addition, the semi-rational solutions are generated to reveal the interaction between lump solutions, soliton solutions, and breather solutions.


2019 ◽  
Vol 33 (28) ◽  
pp. 1950350 ◽  
Author(s):  
Wei-Qi Peng ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang

In this work, we study a generalized (2[Formula: see text]+[Formula: see text]1)-dimensional asymmetrical Nizhnik–Novikov–Veselov (NNV) equation. Its Hirota bilinear form is constructed via the Bell polynomial. Based on the obtained bilinear form, the Nth-order breather waves are derived explicitly under certain parameter constraints. Moreover, we generate the nonsingular Nth-order lump waves through applying the long wave limit method. Additionally, we successfully present the semi-rational waves containing the combination of lump waves and single-soliton waves, the combination of lump waves and breather waves.


2017 ◽  
Vol 72 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Ji-Guang Rao ◽  
Yao-Bin Liu ◽  
Chao Qian ◽  
Jing-Song He

AbstractThe rational and semirational solutions in the Boussinesq equation are obtained by the Hirota bilinear method and long wave limit. It is shown that the rational solutions contain dark and bright rogue waves, and their typical dynamics are analysed and illustrated. The semirational solutions possess a range of hybrid solutions, and the hybrid of rogue wave and solitons are demonstrated in detail by the three-dimensional figures. Under certain parameter conditions, a new kind of semirational solutions consisted of rogue waves, breathers and solitons is discovered, which describes the dynamics of the rogue waves interacting with the breathers and solitons at the same time.


2014 ◽  
Vol 63 (11) ◽  
pp. 110204
Author(s):  
Wang Wei-Gang ◽  
Lin Wan-Tao ◽  
Shi Lan-Fang ◽  
Mo Jia-Qi

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

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