Two-dimensional long wave nonlinear models for the rogue waves in the ocean

Utilizing the Hirota bilinear method, the lump solutions, the interaction solutions with the lump and the stripe solitons, the breathers and the rogue waves for a (3[Formula: see text]+[Formula: see text]1)-dimensional Kudryashov–Sinelshchikov equation are constructed. Two types of interaction solutions between the lumps and the stripe solitons are exhibited. Some different breathers are given by choosing special parameters in the expressions of the solitons. Through a long wave limit of breathers, the lumps and rogue waves are derived.

Download Full-text

Boundary layer collapses described by the two-dimensional intermediate long-wave equation

Theoretical and Mathematical Physics ◽

10.1134/s0040577920040078 ◽

2020 ◽

Vol 203 (1) ◽

pp. 512-523

Author(s):

J. O. Oloo ◽

V. I. Shrira

Keyword(s):

Boundary Layer ◽

Wave Equation ◽

Two Dimensional ◽

Long Wave

Download Full-text

On resonance of an offshore channel bounded by a reef

Marine and Freshwater Research ◽

10.1071/mf9810833 ◽

1981 ◽

Vol 32 (6) ◽

pp. 833 ◽

Cited By ~ 3

Author(s):

VT Buchwald ◽

JW Miles

Keyword(s):

Wave Equations ◽

Amplification Factor ◽

Dominant Mode ◽

Two Dimensional ◽

Barrier Reef ◽

Reef Lagoon ◽

Long Wave ◽

Frictional Damping ◽

Linear Friction ◽

Western Australian

The period and amplification factor for the dominant mode in a channel formed by the shore and a submerged parallel reef (which separates the channel from deeper water) are calculated from the two- dimensional long-wave equations with linear friction. Results are obtained for both narrow and wide reefs and are compared with observed oscillations on the Western Australian coast and on the Barrier Reef. Although the calculated periods might explain the anomalous tides in the Barrier Reef lagoon. it seems that there is sufficient frictional damping to prevent the required amplification.

Download Full-text

Instabilities of three-dimensional viscous falling films

Journal of Fluid Mechanics ◽

10.1017/s0022112092002489 ◽

1992 ◽

Vol 242 ◽

pp. 529-547 ◽

Cited By ~ 86

Author(s):

S. W. Joo ◽

S. H. Davis

Keyword(s):

Evolution Equation ◽

Three Dimensional ◽

Falling Film ◽

Two Dimensional ◽

Wave Evolution ◽

Strongly Nonlinear ◽

Long Wave ◽

Threshold Amplitude ◽

Permanent Wave ◽

Dimensional Wave

A long-wave evolution equation is used to study a falling film on a vertical plate. For certain wavenumbers there exists a two-dimensional strongly nonlinear permanent wave. A new secondary instability is identified in which the three-dimensional disturbance is spatially synchronous with the two-dimensional wave. The instability grows for sufficiently small cross-stream wavenumbers and does not require a threshold amplitude; the two-dimensional wave is always unstable. In addition, the nonlinear evolution of three-dimensional layers is studied by posing various initial-value problems and numerically integrating the long-wave evolution equation.

Download Full-text

Rogue Waves and Hybrid Solutions of the Boussinesq Equation

Zeitschrift für Naturforschung A ◽

10.1515/zna-2016-0436 ◽

2017 ◽

Vol 72 (4) ◽

pp. 307-314 ◽

Cited By ~ 13

Author(s):

Ji-Guang Rao ◽

Yao-Bin Liu ◽

Chao Qian ◽

Jing-Song He

Keyword(s):

Boussinesq Equation ◽

Rogue Wave ◽

Three Dimensional ◽

Rogue Waves ◽

Rational Solutions ◽

Bilinear Method ◽

Long Wave ◽

Hybrid Solutions ◽

Wave Limit ◽

Hirota Bilinear

AbstractThe rational and semirational solutions in the Boussinesq equation are obtained by the Hirota bilinear method and long wave limit. It is shown that the rational solutions contain dark and bright rogue waves, and their typical dynamics are analysed and illustrated. The semirational solutions possess a range of hybrid solutions, and the hybrid of rogue wave and solitons are demonstrated in detail by the three-dimensional figures. Under certain parameter conditions, a new kind of semirational solutions consisted of rogue waves, breathers and solitons is discovered, which describes the dynamics of the rogue waves interacting with the breathers and solitons at the same time.

Download Full-text