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Article

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

1
School of Sciences, University of Southern Queensland, Toowoomba, QLD 4350, Australia
2
Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 603950 Nizhny Novgorod, Russia
Symmetry 2020, 12(10), 1586; https://doi.org/10.3390/sym12101586
Received: 17 August 2020 / Revised: 16 September 2020 / Accepted: 22 September 2020 / Published: 24 September 2020
(This article belongs to the Special Issue Wave Processes in Fluids with Symmetric Density Stratification)
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. View Full-Text
Keywords: Kadomtsev–Petviashvili equation; Benjamin–Ono equation; asymptotic theory; solitary waves; two-soliton solution; phase shift Kadomtsev–Petviashvili equation; Benjamin–Ono equation; asymptotic theory; solitary waves; two-soliton solution; phase shift
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MDPI and ACS Style

Stepanyants, Y. The Asymptotic Approach to the Description of Two-Dimensional Symmetric Soliton Patterns. Symmetry 2020, 12, 1586. https://doi.org/10.3390/sym12101586

AMA Style

Stepanyants Y. The Asymptotic Approach to the Description of Two-Dimensional Symmetric Soliton Patterns. Symmetry. 2020; 12(10):1586. https://doi.org/10.3390/sym12101586

Chicago/Turabian Style

Stepanyants, Yury. 2020. "The Asymptotic Approach to the Description of Two-Dimensional Symmetric Soliton Patterns" Symmetry 12, no. 10: 1586. https://doi.org/10.3390/sym12101586

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