Dynamical analysis of lump solution for the (2+1)-dimensional 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.

Download Full-text

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

Thermal Science ◽

10.2298/tsci16s3919c ◽

2016 ◽

Vol 20 (suppl. 3) ◽

pp. 919-927 ◽

Cited By ~ 2

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.

Download Full-text

The quasi-linear method of fundamental solution applied to non-linear wave equations

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2012.02.016 ◽

2012 ◽

Vol 36 (8) ◽

pp. 1183-1188 ◽

Cited By ~ 7

Author(s):

Mahmood Fallahi

Keyword(s):

Fundamental Solution ◽

Wave Equations ◽

Linear Method ◽

Linear Wave ◽

Non Linear ◽

Linear Wave Equations

Download Full-text

Systematic Experimental Validation of High-Order Spectral Method for Deterministic Wave Prediction

Volume 7B: Ocean Engineering ◽

10.1115/omae2019-95063 ◽

2019 ◽

Author(s):

Marco Klein ◽

Matthias Dudek ◽

Günther F. Clauss ◽

Norbert Hoffmann ◽

Jasper Behrendt ◽

...

Keyword(s):

Spectral Method ◽

Experimental Validation ◽

Linear Method ◽

Wave Spectrum ◽

High Order ◽

Linear Wave ◽

Short Term ◽

Wave Prediction ◽

Non Linear ◽

High Order Spectral Method

Abstract The applicability of the High-Order Spectral Method (HOSM) as a very fast non-linear method for deterministic short-term wave prediction is discussed within this paper. The focus lies on the systematic experimental validation of the HOSM in order to identify and evaluate possible areas of application as well as limitations of use. For this purpose, irregular sea states with varying parameters such as wave steepness and underlying wave spectrum are addressed by numerical simulations and model tests in the controlled environment of a seakeeping basin. In addition, the influence of the propagation distance is discussed. For the evaluation of the accuracy of the HOSM prediction, the surface similarity parameter (SSP) is utilized, allowing a quantitative validation of the results. The results obtained are compared to linear wave prediction to discuss the pros and cons of a non-linear deterministic short-term wave prediction. In conclusion, this paper shows that the non-linear deterministic wave prediction based on HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance.

Download Full-text

Application of Higher Order Spectral Method for Deterministic Wave Forecast

Volume 8B: Ocean Engineering ◽

10.1115/omae2014-24126 ◽

2014 ◽

Cited By ~ 1

Author(s):

Günther F. Clauss ◽

Marco Klein ◽

Matthias Dudek ◽

Miguel Onorato

Keyword(s):

Initial Conditions ◽

Linear Method ◽

Propagation Distance ◽

Higher Order ◽

Experimental Investigations ◽

Linear Wave ◽

Fast Calculation ◽

Wave Forecast ◽

Non Linear ◽

Relative Water

This paper addresses the Higher Order Spectral (HOS) method as very fast and accurate non-linear method for deterministic wave forecast. The focus of the paper lies on wave propagation, with the objective to draw conclusions on the applicability of the HOS method for deterministic wave forecast. Systematic numerical and experimental investigations are conducted. The investigations comprise exact solutions of the nonlinear Schrödinger equation (NLS) as special non-linear wave groups, which are used as initial conditions for the subsequent simulations. Different parameters such as relative water depth, wave steepness and propagation distance are varied to evaluate the applicability of the HOS method. The results obtained are validated by experiments as well as fully non-linear simulations. It is shown that the HOS method is capable for non-linear wave forecast due to high accuracy and fast calculation time at once.

Download Full-text

Non-Linear Wave-Current Interactions in the SWADE Research Program.

Coastal Engineering 1992 ◽

10.1061/9780872629332.030 ◽

1993 ◽

Author(s):

S. P. Kjeldsen ◽

H. C. Graber

Keyword(s):

Research Program ◽

Linear Wave ◽

Non Linear

Download Full-text

Problems on the Gravitational Wave and the Repulsive Gravitation

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v12i4.4403 ◽

2016 ◽

pp. 4422-4429

Author(s):

C. Y. Lo

Keyword(s):

Black Holes ◽

Gravitational Wave ◽

Einstein Equation ◽

Wave Solution ◽

Dynamic Solution ◽

Pure Mathematics ◽

Non Linear

It is exciting that the gravitational wave has been confirmed, according to the announcement of LIGO. This would be the time to fix the Einstein equation for the gravitational wave and the nonexistence of the dynamic solution. As a first step, theorists should improve their pure mathematics on non-linear mathematics and related physical considerations beyond Einstein. Then, it is time to rectify the Einstein equation that has no gravitational wave solution which Einstein has recognized, and no dynamic solution that Einstein failed to see. A problem is that physicists in LIGO did not know their shortcomings. Also, in view of the far distance of the sources, it is very questionable that the physicists can determine they are from black holes. Moreover, since the repulsive gravitation can also generate a gravitational wave, the problem of gravitational wave is actually far more complicated than we have known. A useful feature of the gravitational wave based on repulsive gravitation is that it can be easily generated on earth. Thus this can be a new tool for communication because it can penetrate any medium.

Download Full-text

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

Journal of High Energy Physics ◽

10.1007/jhep01(2021)159 ◽

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.

Download Full-text