Parameter modulation of periodic waves and solitons in metamaterials with higher-order dispersive and nonlinear effects

We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

Download Full-text

Impact of higher order nonlinear effects on modulational instability and pulse train generation in birefringent Lakshmanan–Porsezian–Daniel model

Optik ◽

10.1016/j.ijleo.2021.168462 ◽

2021 ◽

pp. 168462

Author(s):

Gawarai Dieu-donne ◽

C.G. Latchio Tiofack ◽

Malwe Boudoue Hubert ◽

Gambo Betchewe ◽

Doka Yamigno Serge ◽

...

Keyword(s):

Pulse Train ◽

Modulational Instability ◽

Nonlinear Effects ◽

Higher Order ◽

Pulse Train Generation

Download Full-text

Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0275 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Wenying Cui ◽

Yinping Liu ◽

Zhibin Li

Keyword(s):

Fluid Dynamics ◽

Algebraic Method ◽

Higher Order ◽

Decomposition Algorithm ◽

Periodic Waves ◽

Order Interaction ◽

Interaction Solutions ◽

Petviashvili Equation ◽

Bkp Equation ◽

Interaction Phenomena

Abstract In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an N-soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

Download Full-text

Study on the Effect of Climate Change on Ship Responses Based on Nonlinear Simulations

Volume 11B: Honoring Symposium for Professor Carlos Guedes Soares on Marine Technology and Ocean Engineering ◽

10.1115/omae2018-77934 ◽

2018 ◽

Cited By ~ 1

Author(s):

Bingjie Guo ◽

Odin Gramstad ◽

Erik Vanem ◽

Elzbieta Bitner-Gregersen

Keyword(s):

Climate Change ◽

Nonlinear Wave ◽

Structural Reliability ◽

Failure Modes ◽

Bending Moment ◽

Nonlinear Effects ◽

Wave Model ◽

Higher Order ◽

Hull Girder ◽

Structural Rules

Hull girder ultimate strength, which governs sagging and hogging failures, is one of the most critical failure modes for a ship hull. The Structural Reliability Analysis (SRA) methodology has been used to develop Common Structural Rules (CRS) for tankers and bulk carriers. A linear model for bending moment in extreme weather with a nonlinear correction factor has been adopted in the analysis. It is difficult to conclude on the model uncertainty associated with nonlinear effects of bending moment as, until now, there are very limited studies addressing this topic. In this paper, the nonlinear effect on ship responses will be analyzed, and the potential effect of climate change on ship responses will be investigated with the improved 3D Rankine Panel method using nonlinear wave input. The nonlinear wave input is generated by the HOSM (Higher order Spectral Method) wave model incorporating higher order nonlinear effects, including nonlinear free-wave modulation as well as higher order bound harmonics. The North Atlantic past and projected future wave climates are considered.

Download Full-text

Study on the Effect of Climate Change on Ship Responses Based on Nonlinear Simulations

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4042182 ◽

2019 ◽

Vol 141 (4) ◽

Cited By ~ 4

Author(s):

Bingjie Guo ◽

Odin Gramstad ◽

Erik Vanem ◽

Elzbieta Bitner-Gregersen

Keyword(s):

Climate Change ◽

Nonlinear Wave ◽

Structural Reliability ◽

Failure Modes ◽

Bending Moment ◽

Nonlinear Effects ◽

Wave Model ◽

Higher Order ◽

Hull Girder ◽

Structural Rules

Hull girder ultimate strength governs sagging and hogging failures, which is one of the most critical failure modes for a ship hull. The structural reliability analysis methodology has been used to develop common structural rules for tankers and bulk carriers. A linear model for bending moment in extreme weather with a nonlinear correction factor has been adopted in the analysis. It is difficult to conclude on the model uncertainty associated with nonlinear effects of bending moment as, until now, there are few studies addressing this topic. In this paper, the nonlinear effect on ship responses is analyzed, and the potential effect of climate change on ship responses is investigated with the improved three-dimensional (3D) Rankine Panel method using nonlinear wave input. The nonlinear wave input is generated by the higher-order spectral method (HOSM) wave model incorporating higher-order nonlinear effects, including nonlinear free-wave modulation as well as higher-order bound harmonics. The past and projected future wave climates of selected locations in the North Atlantic and North Norwegian Sea are considered.

Download Full-text