THE SOLITARY WAVE THEORY AND ITS APPLICATION TO SURF PROBLEMS

1949 ◽  
Vol 51 (3) ◽  
pp. 376-424 ◽  
Author(s):  
WALTER H. MUNK
Keyword(s):  
Solitary Wave ◽  
Wave Theory

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.

Integral properties of periodic gravity waves of finite amplitude

1975 ◽  
Vol 342 (1629) ◽  
pp. 157-174 ◽  
Keyword(s):  
Solitary Wave ◽  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Cnoidal Wave ◽  
The Mean ◽  
Exact Relations ◽  
Kinetic And Potential Energies

A number of exact relations are proved for periodic water waves of finite amplitude in water of uniform depth. Thus in deep water the mean fluxes of mass, momentum and energy are shown to be equal to 2T(4T—3F) and (3T—2V) crespectively, where T and V denote the kinetic and potential energies and c is the phase velocity. Some parametric properties of the solitary wave are here generalized, and some particularly simple relations are proved for variations of the Lagrangian The integral properties of the wave are related to the constants Q, R and S which occur in cnoidal wave theory. The speed, momentum and energy of deep-water waves are calculated numerically by a method employing a new expansion parameter. With the aid of Padé approximants, convergence is obtained for waves having amplitudes up to and including the highest. For the highest wave, the computed speed and amplitude are in agreement with independent calculations by Yamada and Schwartz. At the same time the computations suggest that the speed and energy, for waves of a given length, are greatest when the height is less than the maximum. In this respect the present results tend to confirm previous computations on solitary waves.

scholarly journals IMPULSE WAVES GENERATED BY LANDSLIDES

1970 ◽  
Vol 1 (12) ◽  
pp. 35 ◽  
Author(s):  
J.W. Kamphuis ◽  
R.J. Bowering
Keyword(s):  
Solitary Wave ◽  
Froude Number ◽  
Wave Height ◽  
Water Surface ◽  
Transition Period ◽  
Wave Theory ◽  
Study Programme ◽  
Long Time ◽  
Velocity Of Propagation ◽  
Impulse Waves

A study programme has been initiated to investigate the impulse waves generated by landslides originating entirely above the water surface It may be seen that the characteristics of this wave depend mainly on the slide volume and the Froude number of the slide upon impact with the water The resulting wave goes through a transition period For the highest wave (usually the first), the wave height becomes stable relatively quickly and decays exponentially during the period of transition, the wave period continues to increase for a long time, the velocity of propagation may be approximated very closely by solitary wave theory.

Exact Traveling Wave Solutions and Bifurcations of Classical and Modified Serre Shallow Water Wave Equations

2019 ◽  
Vol 29 (12) ◽  
pp. 1950153
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Wave Equations ◽  
Wave Theory ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Shallow Water Wave Equations

Using the dynamical systems analysis and singular traveling wave theory developed by Li and Chen [2007] to the classical and modified Serre shallow water wave equations, it is shown that, in different regions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) can be obtained. More than 28 explicit and exact parametric representations are precisely derived. It is demonstrated that, more interestingly, the modified Serre equation has uncountably infinitely many smooth solitary wave solutions and uncountably infinitely many pseudo-peakon solutions. Moreover, it is found that, differing from the well-known peakon solution of the Camassa–Holm equation, the modified Serre equation has four new forms of peakon solutions.

On tsunami and the regularized solitary-wave theory

2010 ◽  
Vol 70 (1-3) ◽  
pp. 137-146 ◽  
Author(s):  
Theodore Yaotsu Wu ◽  
Sunao Murashige
Keyword(s):  
Solitary Wave ◽  
Wave Theory

Bifurcations of Traveling Wave Solutions for Fully Nonlinear Water Waves with Surface Tension in the Generalized Serre–Green–Naghdi Equations

2020 ◽  
Vol 30 (01) ◽  
pp. 2050019
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Water Waves ◽  
Traveling Wave Solutions ◽  
Wave Theory ◽  
Solitary Wave Solutions ◽  
Nonlinear Water Waves ◽  
Fully Nonlinear ◽  
Wave Solutions

For the generalized Serre–Green–Naghdi equations with surface tension, using the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] for their traveling wave systems, in different parameter conditions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) are obtained. More than 26 explicit exact parametric representations are given. It is interesting to find that this fully nonlinear water waves equation coexists with uncountably infinitely many smooth solitary wave solutions or infinitely many pseudo-peakon solutions with periodic solutions or compacton solutions. Differing from the well-known peakon solution of the Camassa–Holm equation, the generalized Serre–Green–Naghdi equations have four new forms of peakon solutions.

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