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Determinant Solutions to a (3+1)-Dimensional Generalized KP Equation with Variable Coefficients

Chinese Annals of Mathematics,Series B 2012年第5期33卷 641-650页

作者： alrazi abdeljabbar Ahmet YILDIRIM Department of Engineering Technology and Mathematics Savannah State University Department of Mathematics and Statistics University of South Florida Department of Mathematics Ege University

1 Introduction Although partial differential equations that govern the motion of solitons are nonlinear, many of them can be put into the bilinear form. Hirota, in 1971, developed an ingenious method to obtain exact solutions to nonlinear partial differential equations in the soliton theory, such as the KdV equation, the Boussinesq equation and the KP equation （see [1-2]）.

关键词： Hirota bilinear form Wronskian solution Grammian solution

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Breather waves, analytical solutions and conservation laws using Lie–Bäcklund symmetries to the (2 + 1)-dimensional Chaffee–Infante equation

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Journal of Ocean Engineering and Science 2023年第2期8卷 145-151页

作者： Abdullahi Yusuf Tukur Abdulkadir Sulaiman alrazi abdeljabbar Marwan Alquran Department of Computer Engineering Biruni University IstanbulTurkey Faculty of Science Federal University DutseJigawaNigeria Department of Mathematics Khalifa University for Science and TechnologyAbu DhabiUAE Department of Mathematics and Statistics Jordan University of Science and TechnologyIrbidJordan

The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,coastal engineering,fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound *** this paper,this equation is investigated and analyzed using two effective *** well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under *** breather wave solutions are derived using the Cole–Hopf *** addition,by means of new conservation theorem,we construct conservation laws(CLs)for the governing equation by means of Lie–Bäcklund *** novel characteristics for the(2+1)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.

关键词： Extended tanh-coth method Sine-cosine function method Soliton solutions Breather wave solutions Conservation laws

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New lump interaction complexitons to the(2+1)-dimensional Korteweg-de Vries equation with electrostatic wave potential in plasmas

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Journal of Ocean Engineering and Science 2024年第2期9卷 173-177页

作者： Tukur Abdulkadir Sulaiman Abdullahi Yusuf alrazi abdeljabbar Mustafa Bayram Department of Computer Engineering Biruni UniversityIstanbulTurkey Department of Mathematics Federal University DutseJigawaNigeria Department of Mathematics Near East University TRNCMersin 10Turkey Department of Mathematics Khalifa University for Science and TechnologyAbu DhabiUAE

A soliton is a packet of self-reinforcing waves that maintains its structure when moving at a constant *** are caused by the cancellation of the medium’s nonlinear and dispersive *** plas-mas,the bilinear form of Hirota will be utilized to investigate the(2+1)-dimensional Korteweg-de Vries equation with electrostatic wave *** for complexiton lump interaction have been *** throw further light on the physical qualities of the recorded data,certain 3-dimensional and contour plots are presented to illustrate the interaction elements of these solutions.

关键词： (2+1)-dimensional Korteweg-de Vries equation Multi waves solutions Brether waves solutions Numerical simulations

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