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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

Solitary Wave Solutions for the Coupled Ito System and a Generalized Hirota-Satsuma Coupled KdV System

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Communications in Theoretical Physics 2001年第12期36卷 657-660页

作者： ZHANG Yu-Feng Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

We make use of an extended tanh-function method and symbolic computation to construct four kinds of travelling solitary wave solutions for the coupled Ito system and a generalized Hirota-Satsuma coupled KdV *** number... 详细信息

关键词： coupled Ito system generalized Hirota-Satsuma coupled KdV system traveling solitary wave solution symbolic computation

On New Invariant Solutions of Generalized Fokker-Planck Equation

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Communications in Theoretical Physics 2004年第5期41卷 665-668页

作者： YAORuo-Xia LIZhi-Bin DepartmentofComputerScience EastChinaNormalUniversityShanghai200062China

The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first repor... 详细信息

关键词： Fokker-Planck equation potential symmetry invariant solutions symbolic computation

New conservation laws and exact solutions of the special case of the fifth-order KdV equation

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Journal of Ocean Engineering and Science 2022年第4期7卷 377-382页

作者： Arzu Akbulut Melike Kaplan Mohammed K.A.Kaabar Department of Mathematics-Computer Art-Science FacultyEskisehir Osmangazi UniversityEskisehirTurkey Department of Mathematics Art-Science FacultyKastamonu UniversityKastamonuTurkey Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia

The current study deals with the Kaup-Kupershmidt(KK)equation to construct formal Lagrangian,con-servation laws,and exact *** is basically a special case of the 5th-order KdV *** conservation laws obtained by using the conservation theorem are trivial conservation *** addition,exact solutions are found via the modified simple equation(MSE)*** a suitable value of solu-tions,the 3D surfaces have been plotted using *** plots giving novel exact solutions are made to reveal important wave *** obtained results in this work concerning our investigated equation are essential to explain many physical and oceanographic applications involving ocean gravity waves and many other related phenomena.

关键词： Conservation laws Exact solutions symbolic computation Modified simple equation method

New Families of Rational Form Variable Separation Solutions to(2+1)-Dimensional Dispersive Long Wave Equations

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Communications in Theoretical Physics 2009年第5期51卷 789-793页

作者： WEN Xiao-Yong Department of Mathematics College of Sciences Beijing Information Science and Technology University Beijing 100192China

With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.

关键词： improved mapping approach variable separation method (2+1)-dimensional dispersive long wave equations symbolic computation

New exact solutions of the Mikhailov-Novikov-Wang equation via three novel techniques

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Journal of Ocean Engineering and Science 2023年第1期8卷 103-110页

作者： Arzu Akbulut Melike Kaplan Mohammed K.A.Kaabar Mathematics-Computer Department Art-Science FacultyEski¸s ehir Osmangazi UniversityEski¸s ehirTurkey Department of Computer Engineering Engineering and Architecture FacultyKastamonu UniversityKastamonuTurkey Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia

The current work aims to present abundant families of the exact solutions of Mikhailov-Novikov-Wang equation via three different *** adopted methods are generalized Kudryashov method(GKM),exponential rational function method(ERFM),and modified extended tanh-function method(METFM).Some plots of some presented new solutions are represented to exhibit wave *** results in this work are essential to understand the physical meaning and behavior of the investigated equation that sheds light on the importance of investigating various nonlinear wave phenomena in ocean engineering and *** equation provides new insights to understand the relationship between the integrability and water waves’phenomena.

关键词： Exact solutions Generalized Kudryashov method Modified extended tanh-function method symbolic computation PDEs

A unique computational investigation of the exact traveling wave solutions for the fractional-order Kaup-Boussinesq and generalized Hirota Satsuma coupled KdV systems arising from water waves and interaction of long waves

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Journal of Ocean Engineering and Science 2024年第5期9卷 437-453页

作者： Xiaofeng Wang Xiao-Guang Yue Mohammed K.A.Kaabar Arzu Akbulut Melike Kaplan Shenzhen University ShenzhenChina Department of Computer Science and Engineering European University CyprusNicosiaCyprus Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia Department of Mathematics and Statistics Washington State UniversityPullmanWA 99163USA Jabalia Camp United Nations Relief and Works Agency(UNRWA)Palestinian Refugee CampGaza Strip JabalyaPalestine Mathematics-Computer Department Art-Science FacultyEski¸s ehir Osmangazi UniversityEski¸s ehirTurkey Department of Computer Engineering Faculty of Engineering and ArchitectureKastamonu UniversityKastamonuTurkey

A novel technique,named auxiliary equation method,is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems:the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional *** solutions were obtained using MAPLE *** technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean *** a standard equation has not been used as an auxiliary equation for this technique,different and novel solutions are obtained via this technique.

关键词： symbolic computation Fractional differential equations Beta derivative Auxiliary equation method Solitary solutions Nonlinear equations

Efficient Algorithm forMany-Electron Angular Momentum and Spin Diagonalization on Atomic Subshells

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Communications in computational Physics 2016年第1期19卷 192-204页

作者： Christian B.Mendl Zentrum Mathematik Technische Universitat MunchenBoltzmannstraße 385748 Garching bei MunchenGermany

We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and u=s,p,d,…denotes the atomic *** is an essential step for dimension reduction in configurationinteraction(CI)methods applied to atomic many-electron quantum *** algorithm relies on the observation that each Lz eigenstate with maximal eigenvalue is also an L2 eigenstate(equivalently for Sz and S2),as well as the traversal of LS eigenstates using the lowering operators L−and S−.Iterative application to the remaining states in∧^(n)V_(u)leads to an implicit simultaneous diagonalization.A detailed complexity analysis for fixed n and increasing subshell number u yields run time O(u^(3n−2)).A symbolic computer algebra implementation is available online.

关键词： Angular momentum and spin symmetry atomic many-electron quantum systems symbolic computation

A New Expanded Method for Solving Nonlinear Differential-difference Equation

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Journal of Shanghai Jiaotong university(Science) 2008年第4期13卷 509-512页

作者：张善卿 Department of Mathematics Shanghai Jiaotong University

A new expanded approach is presented to find exact solutions of nonlinear differential-difference equations. As its application, the soliton solutions and periodic solutions of a lattice equation are obtained.

关键词： differential-difference equation exact solution symbolic computation

Soliton Solutions and Bilinear Bcklund Transformation for Generalized Nonlinear Schrdinger Equation with Radial Symmetry

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Communications in Theoretical Physics 2010年第10期 635-640页

作者：江彦田播刘文军孙鲲屈启兴 School of Science Beijing University of Posts and Telecommunications State Key Laboratory of Software Development Environment Beijing University of Aeronautics and Astronautics Key Laboratory of Information Photonics and Optical Communications(BUPT) Ministry of EducationBeijing University of Posts and Telecommunications

Investigated in this paper is the generalized nonlinear Schrodinger equation with radial symmetry. With the help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method. B^cklund transformation in the bilinear form is presented, through which a new solution is constructed. Graphically, we have found that the solitons are symmetric about x = O, while the soliton pulse width and amplitude will change along with the distance and time during the propagation.

关键词： generalized nonlinear SchrSdinger equation radial symmetry bilinear method symbolic computation soliton solutions Bgcklund transformation