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GLOBAL SOLUTIONS FOR THE GRAVITY WATER WAVES SYSTEM IN 2D
GLOBAL SOLUTIONS THE GRAVITY WATER WAVES SYSTEM 2D
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2014/4/3
We consider the gravity water waves system in the case of a one dimensional interface, for suf- ficiently smooth and localized initial data, and prove global existence of small solutions. This i...
Analytical Solution of Two Extended Model Equations for Shallow Water Waves by He’s Variational Iteration Method
He’s Variational Iteration Method Shallow Water Wave Equation
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2013/1/30
In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for sha...
Particle trajectories beneath small amplitude shallow water waves in constant vorticity flows
Particle trajectories beneath small amplitude constant vorticity flows Fluid Dynamics
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2011/7/26
Abstract: We investigate the particle trajectories in a constant vorticity shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the framework of small amp...
Exact solutions for small-amplitude capillary-gravity water waves
small-amplitude capillary-gravity water waves Fluid Dynamics
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2011/7/26
Abstract: We present explicit solutions for the ordinary differential equations system describing the motion of the particles beneath small-amplitude capillary-gravity waves which propagate on the sur...
Small-amplitude capillary-gravity water waves: exact solutions and particle motion beneath such waves
Small-amplitude capillary-gravity water waves particle motion beneath Fluid Dynamics
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2011/7/26
Abstract: Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitud...
Peakons arising as particle paths beneath small-amplitude water waves
Peakons arising particle paths beneath small-amplitude water waves
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2011/7/26
Abstract: We present a new kind of particle path in constant vorticity water of finite depth, within the framework of small-amplitude waves.
Elliptic and hyperelliptic functions describing the particle motion beneath small-amplitude water waves with constant vorticity
Elliptic hyperelliptic function particle motion beneath small-amplitude water waves
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2011/7/26
Abstract: We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity curr...
Particle trajectories beneath small amplitude shallow water waves in constant vorticity flows
Particle trajectories small amplitude vorticity flows
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2011/9/14
We investigate the particle trajectories in a constant vorticity shallow water flow over a flat bed as periodic waves propagate on the water’s free surface. Within the framework of small amplitude wav...
Exact solutions for small-amplitude capillary-gravity water waves
capillary-gravity water waves Exact solutions
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2011/9/14
We present explicit solutions for the ordinary differential equations system describing the motion of the particles beneath small-amplitude capillary-gravity waves which propagate on the surface of an...
Small-amplitude capillary-gravity water waves: exact solutions and particle motion beneath such waves
capillary-gravity water waves exact solutions particle motion
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2011/9/14
Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, w...
Non-perturbative String Theory from Water Waves
Non-perturbative String Theory Water Waves
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2010/12/24
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regim...
Asymptotic linear stability of solitary water waves
Asymptotic linear stability solitary water waves
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2010/11/29
We prove an asymptotic stability result for the water wave equations linearized around
small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounde...
Fully Nonlinear Shallow Water Waves Simulation Using Green-Naghdi Theory
Green-Naghdi theory model fully nonlinear water waves shoaling waves
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2011/9/8
Green-Naghdi (G-N) theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by “...
Practical use of variational principles for modeling water waves
water waves approximate equations
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2010/4/2
This paper describes a method for deriving approximate equations for water waves. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possibl...
Harmonic Generation of Shallow Water Waves Over Topography
Harmonic Generation Shallow Water Waves Topography
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2009/4/3
We investigate the reflection and nonlinear interaction between the first and second harmonics of a two-dimensional Boussinesq wavetrain. Effects of topography are included, the depth departing from a...