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

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.

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On a homoclinic manifold of a coupled long-wave–short-wave system

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2009.08.017 ◽

2010 ◽

Vol 15 (8) ◽

pp. 2066-2072 ◽

Cited By ~ 2

Author(s):

O.C. Wright

Keyword(s):

Short Wave ◽

Wave System ◽

Long Wave

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Tsunamis

The Physical Geography of the Mediterranean ◽

10.1093/oso/9780199268030.003.0031 ◽

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).

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General high-order breather, lump, and semi-rational solutions to the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation

Modern Physics Letters B ◽

10.1142/s0217984921500573 ◽

2020 ◽

pp. 2150057

Author(s):

Xin-Mei Zhou ◽

Shou-Fu Tian ◽

Ling-Di Zhang ◽

Tian-Tian Zhang

Keyword(s):

Bilinear Form ◽

Soliton Solutions ◽

High Order ◽

Rational Solutions ◽

Lump Solutions ◽

Long Wave ◽

Wave Limit

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.

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ON THE ROLE OF NON-NOETHER SYMMETRY IN INTEGRABILITY OF DISPERSIVELESS LONG WAVE SYSTEM

Mathematical Physics ◽

10.1142/9789812701862_0032 ◽

2005 ◽

Author(s):

G. CHAVCHANIDZE

Keyword(s):

Noether Symmetry ◽

Wave System ◽

Long Wave

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Characteristics of the breather waves, lump waves and semi-rational solutions in a generalized (2+1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

Modern Physics Letters B ◽

10.1142/s0217984919503500 ◽

2019 ◽

Vol 33 (28) ◽

pp. 1950350 ◽

Cited By ~ 1

Author(s):

Wei-Qi Peng ◽

Shou-Fu Tian ◽

Tian-Tian Zhang

Keyword(s):

Bilinear Form ◽

Rational Solutions ◽

Bell Polynomial ◽

Long Wave ◽

Hirota Bilinear Form ◽

Wave Limit ◽

Parameter Constraints ◽

Hirota Bilinear

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.

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Rogue Waves and Hybrid Solutions of the Boussinesq Equation

Zeitschrift für Naturforschung A ◽

10.1515/zna-2016-0436 ◽

2017 ◽

Vol 72 (4) ◽

pp. 307-314 ◽

Cited By ~ 13

Author(s):

Ji-Guang Rao ◽

Yao-Bin Liu ◽

Chao Qian ◽

Jing-Song He

Keyword(s):

Boussinesq Equation ◽

Rogue Wave ◽

Three Dimensional ◽

Rogue Waves ◽

Rational Solutions ◽

Bilinear Method ◽

Long Wave ◽

Hybrid Solutions ◽

Wave Limit ◽

Hirota Bilinear

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.

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