Sloshing in Regular Polygonal Basins—Frequencies, Modes, and Tileability

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Helmholtz Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Small Amplitude ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Shallow Water Waves ◽  
First Time

Abstract The classical theory of small amplitude shallow water waves is applied to regular polygonal basins. The natural frequencies of the basins are related to the eigenvalues of the Helmholtz equation. Exact solutions are presented for triangular, square, and circular basins while pentagonal, hexagonal, and octagonal basins are solved, for the first time, by an efficient Ritz method. The first five eigenvalues of each basin are tabulated and the corresponding mode shapes are discussed. Tileability conditions are presented. Some modes (eigenmodes) can be tiled into larger domains.

scholarly journals The patterns of traveling wave on shallow water modeled by Green-Naghdi equation

2022 ◽  
Vol 355 ◽  
pp. 02005
Author(s):  
Haitong Wei
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Travelling Wave ◽  
Periodic Patterns ◽  
Shallow Water Waves ◽  
Trial Equation Method ◽  
Wave Patterns ◽  
First Time

The Green-Naghdi equations are a shallow water waves model which play important roles in nonlinear wave fields. By using the trial equation method and the Complete discrimination system for the polynomial we obtained the classification of travelling wave patterns. Among those patterns, new singular patterns and double periodic patterns are obtained in the first time. And we draw the graphs which help us to understand the dynamics behaviors of the Green-Naghdi model intuitionally.

Characteristic of the algebraic traveling wave solutions for two extended (2 + 1)-dimensional Kadomtsev–Petviashvili equations

2019 ◽  
Vol 35 (07) ◽  
pp. 2050028 ◽  
Author(s):  
Jian-Gen Liu ◽  
Xiao-Jun Yang ◽  
Yi-Ying Feng
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Traveling Wave Solutions ◽  
Rational Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions ◽  
Restoring Forces ◽  
First Time

With the aid of the planar dynamical systems and invariant algebraic cure, all algebraic traveling wave solutions for two extended (2 + 1)-dimensional Kadomtsev–Petviashvili equations, which can be used to model shallow water waves with weakly nonlinear restoring forces and to describe waves in ferromagnetic media, were obtained. Meanwhile, some new rational solutions are also yielded through an invariant algebraic cure with two different traveling wave transformations for the first time. These results are an effective complement to existing knowledge. It can help us understand the mechanism of shallow water waves more deeply.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

Exact Solutions for a Coupled Korteweg–de Vries System

2016 ◽  
Vol 71 (11) ◽  
pp. 1053-1058
Author(s):  
Da-Wei Zuo ◽  
Hui-Xian Jia
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Type Equation ◽  
Bilinear Forms ◽  
Interfacial Waves ◽  
Rational Solutions ◽  
Shallow Water Waves ◽  
De Vries

AbstractKorteweg–de Vries (KdV)-type equation can be used to characterise the dynamic behaviours of the shallow water waves and interfacial waves in the two-layer fluid with gradually varying depth. In this article, by virtue of the bilinear forms, rational solutions and three kind shapes (soliton-like, kink and bell, anti-bell, and bell shapes) for the Nth-order soliton-like solutions of a coupled KdV system are derived. Propagation and interaction of the solitons are analyzed: (1) Potential u shows three kind of shapes (soliton-like, kink, and anti-bell shapes); Potential v exhibits two type of shapes (soliton-like and bell shapes); (2) Interaction of the potentials u and v both display the fusion phenomena.

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach
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