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Multi-solitons, lumps, and breath solutions of the water wave propagation with surface tension via four recent computational schemes

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AIN SHAMS ENGINEERING JOURNAL 2021年第3期12卷 3031-3041页

作者： Khater, Mostafa M. A. Inc, Mustafa Nisar, K. S. Attia, Raghda A. M. Jiangsu Univ Fac Sci Dept Math Zhenjiang 212013 Jiangsu Peoples R China El Obour Inst Dept Math Cairo 11828 Egypt Firat Univ Sci Fac TR-23119 Elazig Turkey China Med Univ Dept Med Res Taichung Taiwan Prince Sattam Bin Abdulaziz Univ Dept Math Wadi Aldawaser 11991 Saudi Arabia Higher Technol Inst Dept Basic Sci 10th Of Ramadan City Egypt

This research explores the complex and physical behavior, using four different theoretical methods, of water wave propagation with surface tension. A modern Benneye-Luke (BL) algorithm is used to identify a variety of unobtained distinct wave solution forms, such as multi-solitons, lumps and breath-solutions by modified Khater (MK) method, improved Riccati expansion (IRE) method, novel (G'/G) expansion (NGE) method, and generalized Kudryashov (GK) method. The nature of the Hamiltonian method often discusses the properties of the model form. Furthermore, some of the solutions in various forms of plots can be clarified by the complex actions of water wave propagation. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

关键词： Benney-Luke (BL) equation computational schemes Traveling wave solutions Stability

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On the interaction between (low & high) frequency of (ion-acoustic & Langmuir) waves in plasma via some recent computational schemes

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RESULTS IN PHYSICS 2020年 19卷

作者： Khater, Mostafa M. A. Attia, Raghda A. M. Mahmoud, Emad E. Abdel-Aty, Abdel-Haleem Abualnaja, Kholod M. Mohamed, A. -B. A. Eleuch, Hichem Jiangsu Univ Dept Math Fac Sci Zhenjiang 212013 Jiangsu Peoples R China Higher Technol Inst Dept Basic Sci 10th Of Ramadan City 44629 Sharkia Egypt Taif Univ Dept Math & Stat Coll Sci POB 11099 At Taif 21944 Saudi Arabia Sohag Univ Dept Math Fac Sci Sohag 82524 Egypt Univ Bisha Dept Phys Coll Sci POB 344 Bisha 61922 Saudi Arabia Al Azhar Univ Dept Phys Fac Sci Assiut 71524 Egypt Umm Al Qura Univ Fac Sci Appl Dept Math POB 14949 Mecca Saudi Arabia Prince Sattam Bin Abdulaziz Univ Coll Sci & Humanities Al Aflaj Dept Math Al Aflaj Saudi Arabia Assiut Univ Dept Math Fac Sci Assiut Egypt Univ Sharjah Dept Appl Phys & Astron Sharjah U Arab Emirates Abu Dhabi Univ Dept Appl Sci & Math Coll Arts & Sci Abu Dhabi 59911 U Arab Emirates Texas A&M Univ Inst Quantum Sci & Engn College Stn TX 77843 USA

Applying several latest theoretical techniques, the empirical description of the interaction between the high-frequency Langmuir and the low-frequent ion-acoustic waves, derived mathematically by Zakharov's non-dimensional (ZE) equation. These interactions are described in electromagnetic waves, plasma physics, signal processing through optical fibers, coastal engineering, and fluid dynamics. Three modern computing methods are being used to construct several solutions: the extended exp(phi)-expansion process, the popular Kudryashov process, and the modified Khather method. Centered on the properties of the Hamilton system, the stability properties of the solutions are investigated. The physical proprieties are illustrated using 3D plots. The originality of the obtained solutions is explored. We demonstrate that we retrieve the old known solutions and we obtain new solutions that have never been found before.

关键词： The dimensionless form of the Zakharov (ZE) equation The high-frequency Langmuir waves The low-frequency ion-acoustic waves computational schemes Solitonary Solutions Stability property

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THE SOLUTION OF THE NONLINEAR BOLTZMANN-EQUATION - A SURVEY OF ANALYTIC AND computational METHODS

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1995年第7期30卷 21-30页

作者： BELLOMO, N LETALLEC, P PERTHAME, B UNIV PARIS 05 ANAL NUMER LAB F-75270 PARIS FRANCE

This paper provides a survey and a critical overview of the mathematical results, analytic and computational, on the solution of the nonlinear Boltzmann equation. The topics dealt with in this paper are the following: mathematical formulation of initial and/or boundary value problems, existence theorems, computational treatment of fluid dynamical problems.

关键词： BOLTZMANN EQUATION NONLINEAR KINETIC MODELS CAUCHY PROBLEM computational schemes

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An Effective computational Scheme for the Optimal Control of Wave Equations

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IFAC-PapersOnLine 2016年第18期49卷 891-896页

作者： Liu, Jun Li, Buyang Xiao, Mingqing Department of Mathematics and Statistical Sciences Jackson State University JacksonMS39217 United States Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong Hong Kong Department of Mathematics Southern Illinois University IL62901 United States

We proposed and analyzed a new leapfrog finite difference scheme in time for solving the first-order necessary optimality systems arising in optimal control of wave equations. With a standard second-order central finite difference scheme in space, the full discretization is proved to be unconditionally convergent with a second-order accuracy. Moreover, based on its favorable structure, an efficient preconditioned iterative method is provided for solving the discretized unsymmetric sparse linear system. Numerical examples are presented to confirm our theoretical conclusions and demonstrate the promising performance of our proposed algorithms. © 2016

关键词： Wave equations Finite difference method Iterative methods Linear systems Central finite difference computational schemes Finite difference scheme Leap frog schemes Multigrid methods Optimal controls Preconditioned iterative methods Sparse linear systems

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Finite-basis-set optimized effective potential exchange-only method

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JOURNAL OF CHEMICAL PHYSICS 2002年第4期116卷 1269-1276页

作者： Ivanov, S Hirata, S Barlett, RJ Univ Florida Quantum Theory Project Gainesville FL 32611 USA

The finite-basis-set optimized effective potential (OEP) method is presented from an integral equation point of view. It is shown that the projection method for solving the OEP integral equation provides a consistent and convenient approach for including orbital-dependent functionals and potentials in the finite-basis-set implementations of the Kohn-Sham theory. Different finite-basis-set realizations of the OEP method are introduced and tested within the exchange-only approximation. An exact condition involving the local multiplicative exchange potential and the nonlocal Hartree-Fock exchange potential built from Kohn-Sham orbitals is incorporated in our schemes. Numerical results are presented. (C) 2002 American Institute of Physics.

关键词： .OEP projection kernel numerical results KS orbitals realizations exchange potential integral equations exchange-only real symmetric implementations optimized effective potential computational schemes KS theory nite-basis-set functionals and potentials exact condition

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HEREDITARY OPTIMAL-CONTROL PROBLEMS - NUMERICAL-METHOD BASED UPON A PADE-APPROXIMATION

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第1期56卷 157-166页

作者： LEE, AY STANFORD UNIV PALO ALTOCA 94304

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t ? τ). In our approximation scheme, we first replace the variable with an augmented statey(t) ?x(t - τ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.

关键词： Padé approximation hereditary optimal control problems nonlinear time-lag systems computational schemes two-sided Laplace transform gradient algorithms

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OPTIMAL-CONTROL COMPUTATION FOR NONLINEAR TIME-LAG SYSTEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1985年第1期47卷 91-107页

作者： WONG, KH CLEMENTS, DJ TEO, KL UNIV NEW S WALES SCH ELECT ENGN & COMP SCIKENSINGTONNSW 2033AUSTRALIA NATL UNIV SINGAPORE DEPT IND & SYST ENGNSINGAPORE 0511SINGAPORE

In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints... 详细信息

关键词： Control parameterization piecewise constant functions nonlinear hereditary systems linear control constraints computational schemes

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OPTIMAL-CONTROL COMPUTATION FOR LINEAR TIME-LAG SYSTEMS WITH LINEAR TERMINAL CONSTRAINTS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1984年第3期44卷 509-526页

作者： TEO, KL WONG, KH CLEMENTS, DJ UNIV NEW S WALES SCH MATHKENSINGTONNSW 2033AUSTRALIA UNIV NEW S WALES SCH ELECT ENGN & COMP SCIKENSINGTONNSW 2033AUSTRALIA

A computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving linear hereditary systems with bounded control region and linear terminal c... 详细信息

关键词： Control parameterization piecewise constant functions linear time-lag systems linear terminal constraints computational schemes

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ON THE HIERARCHICAL ALGORITHMS FOR NON-LINEAR SYSTEMS WITH BOUNDED CONTROL

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OPTIMAL CONTROL APPLICATIONS & METHODS 1984年第4期5卷 275-288页

作者： MAHMOUD, MS FAWSY, AS MIL TECH COLL DEPT COMP & CONTROLCAIROEGYPT

Hierarchical algorithms for the dynamic optimization of non-linear systems with control bound inequality, constraints are considered. Three different computational schemes are developed, based on the costate prediction co-ordination. Each scheme consists of four levels; of which the second level manipulates the control constraints in an explicit way. Digital simulation of the developed algorithms on a typical power control system is presented.

关键词： Optimal control Non-linear systems Hierarchical algorithms Costate co-ordination computational schemes Power systems

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A FEASIBLE DIRECTIONS ALGORITHM FOR TIME-LAG OPTIMAL-CONTROL PROBLEMS WITH CONTROL AND TERMINAL INEQUALITY CONSTRAINTS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1985年第3期46卷 295-317页

作者： TEO, KL WONG, KH CLEMENTS, DJ UNIV WITWATERSRAND DEPT APPL MATHJOHANNESBURG 2001SOUTH AFRICA UNIV NEW S WALES SCH ELECT ENGN & COMP SCIKENSINGTONNSW 2033AUSTRALIA

A computational algorithm for a class of time-lag optimal control problems involving control and terminal inequality constraints is presented. The convergence properties of the algorithm is also investigated. To test ... 详细信息

关键词： Nonlinear time-lag systems linear control constraints nonlinear terminal inequality constraints conditional gradient methods feasible direction methods control parametrization initial feasible control computational schemes finite convergence

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