A new method for exact solutions of variant types of time-fractional Korteweg-de Vries equations in shallow water waves

2016 ◽  
Vol 40 (1) ◽  
pp. 106-114 ◽  
Author(s):  
S. Sahoo ◽  
S. Saha Ray
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
New Method ◽  
Shallow Water Waves ◽  
De Vries

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.

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 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.

scholarly journals Computational Analysis of Shallow Water Waves with Korteweg-de Vries Equation

2017 ◽  
Vol 0 (0) ◽  
pp. 0-0 ◽  
Author(s):  
Turgut Ak ◽  
Houria Triki ◽  
Sharanjeet Dhawan ◽  
Samir Kumar Bhowmik ◽  
Seithuti Philemon Moshokoa ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Computational Analysis ◽  
Vries Equation ◽  
Shallow Water Waves ◽  
De Vries
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