High-Level Spectral Method for the Fully Nonlinear Waves

Kim, Jang; Park, Sewan; Shen, Zhirong; Kyoung, Johyun; Baquet, Aldric; Lee, Hyungtae; Ha, Yoon-Jin; Park, Jiyong; Kim, Kyong‐Hwan

doi:10.1007/s11804-023-00323-z

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…Nonlinear evolution equations can be used to describe nonlinear phenomena and play a vital role in many fields [1][2][3][4]. Nonlinear science involves the related fields of natural sciences and social sciences, mainly including mathematics, medical chemistry, biology, astronomy, physics, economics and other important subject areas, which is to construct the connection between mathematics and other disciplines.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Zhang,

Bao

2024

Preprint

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In this article, we employ the Bell polynomial method to construct its bilinear form, bilinear Bäcklund transformation, Lax pair, the integrability, infinite conservation laws and superposition formula of the generalized (2 + 1)-dimensional variable-coefficient fifth-order KdV equation, which can help us get more properties, increase the diversity of solutions and get more new phenomenon. It applies the Lax pairs to test the complete integrability of the generalized (2 + 1) -dimensional variable-coefficient fifth-order KdV equation. According to the obtained bilinear Bäcklund transformation, infinite conservation laws and nonlinear superposition formula are derived. By using the nonlinear superposition formula of the solution, the double soliton solution is obtained from the single soliton solution of the equation. Utilizing a symbolic computation approach, we get the Lump solution and exponential of compound solution, breather-type solution and rouge wave solution with appropriate values of constant coefficients. The generalized (2 + 1)-dimensional variable - coefficient fifth-order KdV equation analyses the evolution of long waves with modest amplitudes propagating in plasma physics and the motion of waves in fluids and other mediums. Moreover, dusty plasma, oceanography, water engineering, and other nonlinear sciences.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Zhang,

Bao

2024

Preprint

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Hydrodynamic Characteristics of Offshore Wind Turbine Pile Foundations Under Combined Focusing Wave-Current Conditions

Ji,

Li,

et al. 2024

JMSE

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In extreme marine environments, the interaction between offshore wind turbine pile foundations (OWTPFs) is critical, and the associated hydrodynamic loads are complex. This study focused on fixed OWTPFs and used computational fluid dynamics (CFD) to numerically simulate the flow field around pile foundations under the combined action of focusing waves and current. The objective was to investigate the influence of different focusing wave and current parameters on the hydrodynamic properties of the pile foundations. The findings indicate the following: (1) When the wave and current directions are opposite, the maximum wave force on the pile foundations is greater than when they are aligned. (2) Large-amplitude focusing waves around pile foundations generate secondary loads, which are nonlinear and lead to a rapid increase in the wave force. These secondary loads are short-lived and particularly prominent near the front row of pile foundations. (3) The influence of the group pile effect diminishes under high-amplitude waves, where the wave component dominates the generation of the dimensionless wave force, and the impact of the current on this force decreases.

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High-Level Spectral Method for the Fully Nonlinear Waves

Cited by 2 publications

References 18 publications

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Hydrodynamic Characteristics of Offshore Wind Turbine Pile Foundations Under Combined Focusing Wave-Current Conditions

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