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Bilinear forms through the binary Bell polynomials, N solitons and Backlund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach

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Communications in Theoretical Physics 2020年第9期72卷 8-12页

作者： Xin-Yi Gao Yong-Jiang Guo Wen-Rui Shan State Key Laboratory of Information Photonics and Optical Communications and School of ScienceBeijing University of Posts and TelecommunicationsBeijing 100876China

water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-B?cklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and B?cklund transformations are different from those in the existing literature. All of our results are dependent on the waterwave dispersive power.

关键词： lakes and ocean beaches shallow water waves Boussinesq–Burgers system symbolic computation bilinear forms through the binary Bell polynomials Backlund transformations solitonic solutions

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Painlevé integrability and a collection of new wave structures related to an important model in shallow water waves

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理论物理通讯:英文版 2023年第7期75卷 70-80页

作者： Isma Ghulam Murtaza Nauman Raza Saima Arshed Department of Mathematics University of the PunjabLahore 54590Pakistan

This paper investigates the perturbed Boussinesq equation that emerges in shallow water *** perturbed Boussinesq equation describes the properties of longitudinal waves in bars,long water waves,plasma waves,quantum mechanics,acoustic waves,nonlinear optics,and other *** a result,the governing model has significant importance in its own *** singular manifold method and the unified methods are employed in the proposed model for extracting hyperbolic,trigonometric,and rational function *** solutions may be useful in determining the underlying context of the physical *** is worth noting that the executed methods are skilled and effective for examining nonlinear evaluation equations,compatible with computer algebra,and provide a wide range of wave *** addition to this,the Painlevétest is also used to check the integrability of the governing ***-dimensional and threedimensional plots are made to illustrate the physical behavior of the newly obtained exact *** makes the study of exact solutions to other nonlinear evaluation equations using the singular manifold method and unified technique prospective and deserving of further study.

关键词： soliton shallow water waves singular manifold method Painleve test

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Surface Gravity waves: shallow water Fluid Particle Physics

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Natural Science 2020年第10期12卷 681-683页

作者： Kern E. Kenyon 4632 North Lane Del Mar CA USA

One of Newton’s mathematical solutions to a hypothetical orbital problem, recently verified by an independent physics model, is applied to the fluid particle motion in shallow water surface gravity waves. What is the functional form of the central force, with origin at the ellipse’s center, which will keep a body in the orbit? Newton found out it is the spring force, which is linear. All fluid particles in shallow water waves move in ellipses. By a superposition of solutions in a linear problem, the application of Newton’s result to shallow water waves is combined with a feature not noticed by Newton: the orbital period is independent of the semi-major and semi-minor axes. Two conclusions reached are that the wave period of shoaling waves should be constant and that there is no friction in these waves.

关键词： shallow water waves Fluid Particle Physics

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NUMERICAL MODELING OF WAVE EVOLUTION AND RUNUP IN shallow water

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Journal of Hydrodynamics 2009年第6期21卷 731-738页

作者： DONG Zhi ZHAN Jie-min Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou 510275 China Guangdong Province Key Laboratory of Coastal Ocean Engineering Sun Yat-sen University Guangzhou 510275China

Based on the Navier-Stokes （N-S） equations for viscous, incompressible fluid and the VOF method, 2-D and 3-D Numerical Wave Tanks （NWT） for nonlinear shallow water waves are built. The dynamic mesh technique is applied, which can save computational resources dramatically for the simulation of solitary wave propagating at a constant depth. Higher order approximation for cnoidal wave is employed to generate high quality waves. Shoaling and breaking of solitary waves over different slopes are simulated and analyzed systematically. Wave runup on structures is also investigated. The results agree very well with experimental data or analytical solutions.

关键词： VOF method shallow water waves wave evolution wave runup

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Applying the New Extended Direct Algebraic Method to Solve the Equation of Obliquely Interacting waves in shallow waters

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Journal of Ocean University of China 2020年第4期19卷 772-780页

作者： KURT Ali TOZAR Ali TASBOZAN Orkun Department of Mathematics Faculty of Science and ArtPamukkale UniversityDenizli 20160Türkiye Department of Physic Faculty of Science and ArtMustafa Kemal UniversityHatay 31001Türkiye Department of Mathematics Faculty of Science and ArtMustafa Kemal UniversityHatay 31001Türkiye

In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic *** results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be *** article fairly clarifies the behaviors of surface waves in shallow *** the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great ***,this study will serve as a reference to guide scientists working in this field.

关键词： conformable fractional derivative new extended direct algebraic method interacting wave equation shallow water waves

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Solution of KdV and mKdV Equationsusing Darboux Transformation

Solution of KdV and mKdV Equationsusing Darboux Transformati...

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作者： Wael Sulayman Miftah Ammar 浙江科技学院

学位级别：硕士

Internal solitary waves(ISWs)are common in the ocean and perform vital functions in a variety of ways,including mass and nutrient movement via *** history of an initial solitary wave solved by a completely nonlinear model,modified model,and Darboux transformation model is observed and compared to the evolution for the weakly nonlinear wave equations,the KDV *** waves or solitons as solutions to the Korteweg-de Vries equation(Kd V)and the mordified-Korteweg-de Vries equation(m Kd V)which are non-linear partial differential equations(PDE)of third order have been of interest already since 150 *** this thesis some of the methods used in solving this equations were observed and collected,the derivation of the equations were observed and the Darboux transformation of the equations was also *** applications of the equation in engineering simulation was investigated by employing the Homotopy perturbation transform method(HPTM)for solving the generic model of nonlinear fifth order Kd V equations for the study of magneto-acoustic waves in plasma.

关键词： shallow water waves Solutions KDV equations Solutions m KDV equations Darboux Transformations HPTM

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