scholarly journals Evolutionary dynamics of solitary wave profiles and abundant analytical solutions to a (3+1)-dimensional Burgers system in ocean physics and hydrodynamics

2021 ◽  
Author(s):  
Sachin Kumar ◽  
Amit Kumar ◽  
Brij Mohan
Keyword(s):  
Solitary Wave ◽  
Analytical Solutions ◽  
Evolutionary Dynamics ◽  
Wave Profiles ◽  
Ocean Physics ◽  
Burgers System

On the recovery of solitary wave profiles from pressure measurements

2012 ◽  
Vol 699 ◽  
pp. 376-384 ◽  
Author(s):  
A. Constantin
Keyword(s):  
Solitary Wave ◽  
Explicit Formula ◽  
Large Amplitude ◽  
Water Wave ◽  
Pressure Measurements ◽  
Pressure Data ◽  
Governing Equations ◽  
Wave Profiles

AbstractWe derive an explicit formula that permits the recovery of the profile of an irrotational solitary water wave from pressure data measured at the flat bed of the fluid domain. The formula is valid for the governing equations and applies to waves of small and large amplitude.

A Generalized Sub-Equation Expansion Method and Some Analytical Solutions to the Inhomogeneous Higher-Order Nonlinear Schrödinger Equation

2008 ◽  
Vol 63 (12) ◽  
pp. 763-777 ◽  
Author(s):  
Biao Li ◽  
Yong Chen ◽  
Yu-Qi Li
Keyword(s):  
Solitary Wave ◽  
Analytical Solutions ◽  
Elliptic Function ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
High Order ◽  
Solitary Wave Solutions ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

On the basis of symbolic computation a generalized sub-equation expansion method is presented for constructing some exact analytical solutions of nonlinear partial differential equations. To illustrate the validity of the method, we investigate the exact analytical solutions of the inhomogeneous high-order nonlinear Schrödinger equation (IHNLSE) including not only the group velocity dispersion, self-phase-modulation, but also various high-order effects, such as the third-order dispersion, self-steepening and self-frequency shift. As a result, a broad class of exact analytical solutions of the IHNLSE are obtained. From our results, many previous solutions of some nonlinear Schrödinger-type equations can be recovered by means of suitable selections of the arbitrary functions and arbitrary constants. With the aid of computer simulation, the abundant structure of bright and dark solitary wave solutions, combined-type solitary wave solutions, dispersion-managed solitary wave solutions, Jacobi elliptic function solutions and Weierstrass elliptic function solutions are shown by some figures.

Bell Waves and Kind Waves for a (1+1)-Dimensional Nonlinear Partial Differential Equation

2013 ◽  
Vol 273 ◽  
pp. 831-834
Author(s):  
Qing Bao Ren ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Nonlinear Partial Differential Equation ◽  
Variable Separation ◽  
New Family ◽  
Variable Separation Approach ◽  
Burgers System

With the help of the symbolic computation system Maple and the mapping approach and a linear variable separation approach, a new family of exact solutions of the (1+1)-dimensional Burgers system is derived. Based on the derived solitary wave solution, some novel bell wave and kind wave excitations are investigated.

Boundary layer flow and bed shear stress under a solitary wave

2007 ◽  
Vol 574 ◽  
pp. 449-463 ◽  
Author(s):  
PHILIP L.-F. LIU ◽  
YONG SUNG PARK ◽  
EDWIN A. COWEN
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Solitary Wave ◽  
Analytical Solutions ◽  
Boundary Layer Flow ◽  
Inertia Force ◽  
Bed Shear Stress ◽  
Viscous Boundary Layer ◽  
Layer Flow ◽  
Viscous Boundary

Liu & Orfila (J. Fluid Mech. vol. 520, 2004, p. 83) derived analytical solutions for viscous boundary layer flows under transient long waves. Their analytical solutions were obtained with the assumption that the nonlinear inertia force was negligible in the momentum equations. In this paper, using Liu & Orfila's solution and the solutions for the nonlinear boundary layer equations, we examine the boundary layer flow characteristics under a solitary wave. It is found that while the horizontal component of the free-stream velocity outside the boundary layer always moves in the direction of wave propagation, the fluid particle velocity near the bottom inside the boundary layer reverses direction as the wave decelerates. Consequently, the bed shear stress also changes sign during the deceleration phase. Laboratory measurements, including the free-surface displacement, particle image velocimetry (PIV) resolved velocity fields of the viscous boundary layer, and the calculated bed shear stress were also collected to check the theoretical results. Excellent agreement is observed.

Abundant analytical solutions of the fractional nonlinear (2 + 1)-dimensional BLMP equation arising in incompressible fluid

2020 ◽  
Vol 34 (09) ◽  
pp. 2050084 ◽  
Author(s):  
Chen Yue ◽  
Mostafa M. A. Khater ◽  
Mustafa Inc ◽  
Raghda A. M. Attia ◽  
Dianchen Lu
Keyword(s):  
Solitary Wave ◽  
Incompressible Fluid ◽  
Physical Properties ◽  
Analytical Solutions ◽  
Stability Property ◽  
Dynamical Behavior ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Physical Experiments ◽  
The Stability

New analytical wave solutions are investigated of the fractional nonlinear [Formula: see text]-dimensional Boiti–Leon–Manna–Pempinelli equation to explain more physical properties of the dynamical behavior of the incompressible fluid. A new fractional definition is used through the modified Khater method to get novel solitary wave solutions of this model. The stability property of the obtained solutions is tested to show the ability of our obtained solutions in using through the physical experiments. The novelty and advantage of the proposed method are illustrated by applying to this model. Some sketches are plotted to show more about the dynamical performance of this model.

Some Exact Analytical Solutions to the Inhomogeneous Higher-Order Nonlinear Schrödinger Equation Using Symbolic Computation

2006 ◽  
Vol 61 (10-11) ◽  
pp. 509-518 ◽  
Author(s):  
Biao Li ◽  
Yong Chen
Keyword(s):  
Solitary Wave ◽  
Symbolic Computation ◽  
Analytical Solutions ◽  
Group Velocity Dispersion ◽  
Broad Class ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

In this paper, the generalized projective Riccati equation method is extended to investigate the inhomogeneous higher-order nonlinear Schrödinger (IHNLS) equation including not only the group velocity dispersion and self-phase-modulation, but also various higher-order effects, such as the third-order dispersion, self-steepening and self-frequency shift. With the help of symbolic computation, a broad class of analytical solutions of the IHNLS equation is presented, which include bright-like solitary wave solutions, dark-like solitary wave solutions, W-shaped solitary wave solutions, combined bright-like and dark-like solitary wave solutions, and dispersion-managed solitary wave solutions. From our results, many previously known results about the IHNLS equation can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Furthermore, from the soliton management concept, the main soliton-like character of the exact analytical solutions is discussed and simulated by computer under different parameters conditions.

scholarly journals Construction of New Exact Solutions for the (3 + 1)-Dimensional Burgers System

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Zitian Li
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Separation Method ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Variable Separation Method ◽  
Burgers System

By means of a variable separation method and a generalized direct ansätz function approach, new exact solutions including cross kink-wave solutions, doubly periodic kinky-wave solutions, and breather type of two-solitary wave solutions for the (3 + 1)-dimensional Burgers system are obtained. Moreover, the mechanical features are also investigated.

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