scholarly journals Self-similarity transformation and two-dimensional rogue wave construction of non-autonomous Kadomtsev-Petviashvili equation

2020 ◽  
Vol 69 (24) ◽  
pp. 244205-244205
Author(s):  
Zhang Jie-Fang ◽  
◽  
Jin Mei-Zhen ◽  
Hu Wen-Cheng ◽  
◽  
...  
Keyword(s):  
Similarity Transformation ◽  
Rogue Wave ◽  
Two Dimensional ◽  
Self Similarity ◽  
Petviashvili Equation

scholarly journals Two-dimensional self-similarity transformation theory and line rogue waves excitation

2022 ◽  
Vol 71 (1) ◽  
pp. 014205-014205
Author(s):  
Zhang Jie-Fang ◽  
◽  
Yu Ding-Guo ◽  
Jin Mei-Zhen ◽  
◽  
...  
Keyword(s):  
Similarity Transformation ◽  
Rogue Waves ◽  
Two Dimensional ◽  
Transformation Theory ◽  
Self Similarity

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

scholarly journals The Asymptotic Approach to the Description of Two-Dimensional Symmetric Soliton Patterns

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1586
Author(s):  
Yury Stepanyants
Keyword(s):  
Solitary Waves ◽  
Asymptotic Theory ◽  
Deep Ocean ◽  
Two Dimensional ◽  
Asymptotic Approach ◽  
Suggested Approach ◽  
Symmetric Wave ◽  
Petviashvili Equation ◽  
Wave Patterns ◽  
Symmetric Soliton

The asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe stationary moving symmetric wave patterns consisting of two plane solitary waves of equal amplitudes moving at an angle to each other. The results obtained within the approximate asymptotic theory are validated by comparison with the exact two-soliton solution of the Kadomtsev–Petviashvili equation (KP2-equation). The suggested approach is equally applicable to a wide class of non-integrable equations too. As an example, the asymptotic theory is applied to the description of wave patterns in the 2D Benjamin–Ono equation describing internal waves in the infinitely deep ocean containing a relatively thin one of the layers.

Breather wave, rogue wave and lump wave solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid

2018 ◽  
Vol 32 (20) ◽  
pp. 1850223 ◽  
Author(s):  
Ming-Zhen Li ◽  
Bo Tian ◽  
Yan Sun ◽  
Xiao-Yu Wu ◽  
Chen-Rong Zhang
Keyword(s):  
Wave Velocity ◽  
Water Waves ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Dispersion Effect ◽  
Wave Solutions ◽  
Weak Perturbation ◽  
Petviashvili Equation ◽  
Nonlinearity Effect ◽  
Lump Wave

Under investigation in this paper is a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili equation, which describes the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in a fluid. Via the Hirota method and symbolic computation, the lump wave, breather wave and rogue wave solutions are obtained. We graphically present the lump waves under the influence of the dispersion effect, nonlinearity effect, disturbed wave velocity effects and perturbed effects: Decreasing value of the dispersion effect can lead to the range of the lump wave decreases, but has no effect on the amplitude. When the value of the nonlinearity effect or disturbed wave velocity effects increases respectively, lump wave’s amplitude decreases but lump wave’s location keeps unchanged. Amplitudes of the lump waves are independent of the perturbed effects. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity. When the value of the dispersion effect decreases, range of the rogue wave increases. When the value of the nonlinearity effect or disturbed wave velocity effects decreases respectively, rogue wave’s amplitude decreases. Value changes of the perturbed effects cannot influence the rogue wave.

Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions

2009 ◽  
Vol 465 (2109) ◽  
pp. 2725-2749 ◽  
Author(s):  
M. J. Ablowitz ◽  
T. S. Haut
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Asymptotic Series ◽  
High Order ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Small Surface ◽  
Petviashvili Equation ◽  
Dimensional Series

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech 2 solution of the Korteweg–de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev–Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes’ extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney–Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

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