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

Traveling Wave Solutions of a Two-Component Dullin–Gottwald–Holm System

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Jiyu Zhong ◽  
Shengfu Deng
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Planar Systems

In this paper, we investigate the traveling wave solutions of a two-component Dullin–Gottwald–Holm (DGH) system. By qualitative analysis methods of planar systems, we investigate completely the topological behavior of the solutions of the traveling wave system, which is derived from the two-component Dullin–Gottwald–Holm system, and show the corresponding phase portraits. We prove the topological types of degenerate equilibria by the technique of desingularization. According to the dynamical behaviors of the solutions, we give all the bounded exact traveling wave solutions of the system, including solitary wave solutions, periodic wave solutions, cusp solitary wave solutions, periodic cusp wave solutions, compactonlike wave solutions, and kinklike and antikinklike wave solutions. Furthermore, to verify the correctness of our results, we simulate these bounded wave solutions using the software maple version 18.

Pseudo-Peakon, Periodic Peakons and Compactons on a Shallow Water Model with Coriolis Effect

2021 ◽  
Vol 31 (08) ◽  
pp. 2150144
Author(s):  
Zhenshu Wen ◽  
Guanrong Chen ◽  
Jibin Li
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Solitary Wave Solution ◽  
Wave Theory ◽  
Water Model ◽  
Wave System ◽  
Coriolis Effect ◽  
Bounded Solutions ◽  
Shallow Water Model

For a shallow water model with Coriolis effect, by applying the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to its traveling wave system, under different parameter conditions, all possible bounded solutions (solitary wave solution, pseudo-peakon and periodic peakons as well as compactons) are obtained. Some exact explicit parametric representations are presented.

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).

Lump and interactional solutions of the (2+1)-dimensional generalized breaking soliton equation

2019 ◽  
Vol 34 (03) ◽  
pp. 2050037
Author(s):  
Yu-Pei Fan ◽  
Ai-Hua Chen
Keyword(s):  
Solitary Wave ◽  
Asymptotic Analysis ◽  
Bilinear Form ◽  
Lump Solution ◽  
Soliton Equation ◽  
Long Wave ◽  
Wave Limit

In this paper, by using the long wave limit method, we study lump solution and interactional solution of the (2[Formula: see text]+[Formula: see text]1)-dimensional generalized breaking soliton equation without using bilinear form. The moving properties of the lump solution, and the interactional properties of a lump and a solitary wave, are analyzed theoretically and graphically with asymptotic analysis.

Solitary wave solutions, lump solutions and interactional solutions to the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation

2020 ◽  
Vol 34 (07) ◽  
pp. 2050053
Author(s):  
Min Gao ◽  
Hai-Qiang Zhang
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Lump Solution ◽  
Solitary Wave Solutions ◽  
Bilinear Method ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Dimensional Equation ◽  
Hirota Bilinear ◽  
Bkp Equation

In this paper, we investigate a [Formula: see text]-dimensional B-type Kadomtsev-Petviashvili (BKP) equation, which is a generalization of the [Formula: see text]-dimensional equation. Based on the Hirota bilinear method and the limit technique of long wave, we systematically construct a family of exact solutions of BKP equation including the [Formula: see text]-solitary wave solution, lump solution as well as interaction solution between lump waves and solitary waves.

Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models

2020 ◽  
Vol 30 (03) ◽  
pp. 2050036 ◽  
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Two Component ◽  
Wave Models

For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa–Holm equation, it is found that its [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].

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