scholarly journals Kink degeneracy and rogue potential flow for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 919-927 ◽  
Author(s):  
Han-Lin Chen ◽  
Zhen-Hui Xu ◽  
Zheng-De Dai
Keyword(s):  
Potential Flow ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Linear Wave ◽  
Test Technique ◽  
Rational Potential ◽  
Higher Dimensional ◽  
Petviashvili Equation ◽  
Non Linear ◽  
Kink Soliton

The breather-type kink soliton, breather-type periodic soliton solutions and rogue potential flow for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are obtained by using the extended homoclinic test technique and homoclinic breather limit method, respectively. Furthermore, some new non-linear phenomena, such as kink and periodic degeneracy, are investigated and the new rational breather solutions are found out. Meanwhile, we also obtained the rational potential solution and it is just a rogue wave. These results enrich the variety of the dynamics of higher-dimensional non-linear wave field.

scholarly journals Dynamical analysis of lump solution for the (2+1)-dimensional Ito equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1673-1679 ◽  
Author(s):  
Wei Tan ◽  
Zheng-De Dai ◽  
Hou-Ping Dai
Keyword(s):  
Wave Solution ◽  
Linear Method ◽  
Perturbation Parameter ◽  
Dynamical Analysis ◽  
Lump Solution ◽  
Linear Wave ◽  
Test Technique ◽  
Higher Dimensional ◽  
Non Linear ◽  
Ito Equation

Exact kinky breather-wave solution, periodic breather-wave solution, and some lump solutions to the (2+1)-dimensional Ito equation are obtained by using an extended homoclinic test technique and Hirota bi-linear method with a perturbation parameter u0. Furthermore, a new non-linear phenomenon in the lump solution, is investigated and discussed. These interesting non-linear phenomena might provide us with useful information on the dynamics of higher-dimensional non-linear wave field.

Lump and rogue waves for the variable-coefficient Kadomtsev–Petviashvili equation in a fluid

2018 ◽  
Vol 32 (10) ◽  
pp. 1850086 ◽  
Author(s):  
Xiao-Yue Jia ◽  
Bo Tian ◽  
Zhong Du ◽  
Yan Sun ◽  
Lei Liu
Keyword(s):  
Small Amplitude ◽  
Variable Coefficient ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Single Layer ◽  
Rogue Waves ◽  
Variable Coefficients ◽  
The Other ◽  
Transverse Coordinate ◽  
Petviashvili Equation

Under investigation in this paper is the variable-coefficient Kadomtsev–Petviashvili equation, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid. Employing the bilinear form and symbolic computation, we obtain the lump, mixed lump-stripe soliton and mixed rogue wave-stripe soliton solutions. Discussions indicate that the variable coefficients are related to both the lump soliton’s velocity and amplitude. Mixed lump-stripe soliton solutions display two different properties, fusion and fission. Mixed rogue wave-stripe soliton solutions show that a rogue wave arises from one of the stripe solitons and disappears into the other. When the time approaches 0, rogue wave’s energy reaches the maximum. Interactions between a lump soliton and one-stripe soliton, and between a rogue wave and a pair of stripe solitons, are shown graphically.

Exact propagating multi-anti-kink soliton solutions of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2015 ◽  
Vol 83 (3) ◽  
pp. 1453-1462 ◽  
Author(s):  
M. T. Darvishi ◽  
M. Najafi ◽  
S. Arbabi ◽  
L. Kavitha
Keyword(s):  
Soliton Solutions ◽  
Petviashvili Equation ◽  
Kink Soliton

Rational and semi-rational solutions for the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation

2019 ◽  
Vol 33 (25) ◽  
pp. 1950296 ◽  
Author(s):  
Ya-Si Deng ◽  
Bo Tian ◽  
Yan Sun ◽  
Chen-Rong Zhang ◽  
Cong-Cong Hu
Keyword(s):  
Water Waves ◽  
Boussinesq Equation ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Different Shapes ◽  
Lump Wave ◽  
Kink Soliton

Nonlinear waves are seen in nature, such as the water waves and plasma waves. Investigated in this paper is a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Based on the bilinear method, we get the rational solutions, which are different from the published ones, semi-rational solutions and breather-type kink soliton solutions. Through the rational solutions, we observe two types of waves: the lump waves and line rogue waves. The semi-rational solutions depict two types of interactions: (1) The fusion or fission between the lump wave and soliton; (2) The interaction between the line rogue wave and soliton. During the interaction between the line rogue wave and soliton, the line rogue wave evolves with three different shapes: the bright rogue waves, bright–dark rogue waves and dark rogue waves. Via the breather-type kink soliton solutions, we observe the breather-soliton mixture.

scholarly journals Influence of Viscosity and Non-Linearities in Predicting Motions of a Wind Energy Offshore Platform in Regular Waves

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
José del Águila Ferrandis ◽  
Luca Bonfiglio ◽  
Ricardo Zamora Rodríguez ◽  
Chryssostomos Chryssostomidis ◽  
Odd Magnus Faltinsen ◽  
...  
Keyword(s):  
Boundary Element ◽  
Potential Flow ◽  
Offshore Platform ◽  
Operating Conditions ◽  
Boundary Element Methods ◽  
Linear Wave ◽  
Floating Bodies ◽  
Computational Costs ◽  
Non Linear ◽  
Flow Theories

Abstract Motion predictions of floating bodies in extreme waves represent a challenging problem in naval hydrodynamics. The solution of the seakeeping problem involves the study of complex non-linear wave-body interactions that require large computational costs. For this reason, over the years, many seakeeping models have been formulated in order to predict ship motions using simplified flow theories, usually based on potential flow theories. Neglecting viscous effects in the wave-induced forces might largely underestimate the energy dissipated by the system. This problem is particularly relevant for unconventional floating bodies at resonance. In these operating conditions, the linear assumption is no longer valid, and conventional boundary element methods, based on potential flow, might predict unrealistic large responses if not corrected with empirical viscous damping coefficients. The application considered in this study is an offshore platform to be operated in a wind farm requiring operability even in extreme meteorological conditions. In this paper, we compare heave and pitch response amplitude operators predicted for an offshore platform using three different seakeeping models of increasing complexity, namely, a frequency-domain boundary element method (BEM), a partly nonlinear time domain BEM, and a non-linear viscous model based on the solution of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. Results are critically compared in terms of accuracy, applicability, and computational costs.

scholarly journals Quantum corrections to generic branes: DBI, NLSM, and more

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Garrett Goon ◽  
Scott Melville ◽  
Johannes Noller
Keyword(s):  
Sigma Models ◽  
Quantum Corrections ◽  
Higher Dimensional ◽  
Symmetry Properties ◽  
Non Linear ◽  
Quantum Action ◽  
Manifest Covariance ◽  
Linear Sigma Models ◽  
Scalar Sector ◽  
Explicit Comparison

Abstract We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

scholarly journals Excitation Forces Estimation for Non-linear Wave Energy Converters: A Neural Network Approach

2020 ◽  
Vol 53 (2) ◽  
pp. 12334-12339
Author(s):  
M. Bonfanti ◽  
F. Carapellese ◽  
S.A. Sirigu ◽  
G. Bracco ◽  
G. Mattiazzo
Keyword(s):  
Neural Network ◽  
Wave Energy ◽  
Linear Wave ◽  
Network Approach ◽  
Neural Network Approach ◽  
Wave Energy Converters ◽  
Non Linear ◽  
Energy Converters

Two integrable extensions of the Kadomtsev-Petviashvili equation

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Completely Integrable ◽  
Multiple Soliton Solutions ◽  
Petviashvili Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractIn this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.

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