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Computer classification of integrable coupled KdV-like systems

V.P. Gerdt, D.Yu. Zharkov
1990 Journal of symbolic computation  
Within the framework of the symmetry approach the ten-parametric family of the third order non-linear evolution coupled KdV-like systems is investigated.  ...  This allows us to obtain the complete list of integrable systems of a given type. All computation has been completed on the basis of computer algebra systems FORMAC and REDUCE.  ...  In the present paper we use computer algebra to find all integrable coupled KdV-like evolution systems.  ... 
doi:10.1016/s0747-7171(08)80041-7 fatcat:wyaoskyhkffl5o776do7k7bpii

Page 825 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews  
(RS-SART; Saratov) Computer classification of the integrable coupled KdV-like systems with unit main matrix. (English summary) J. Symbolic Comput. 15 (1993), no. 1, 85-90.  ...  A new class of such integrable KdV-like systems is obtained.  ... 

Page 5273 of Mathematical Reviews Vol. , Issue 90I [page]

1990 Mathematical Reviews  
Summary: “A system of algebraic equations which follows from the necessary integrability conditions for a ten-parameter family of coupled KdV-like nonlinear evolution systems is considered.  ...  As a result we obtain the complete list of integrable coupled KdV-like systems.” 90i1:58069 58F07 35Q20 82A40 Gibbons, John (4-LNDIC); Kupershmidt, Boris A. (1-TNT) Kinetic representation of the KP hierarchy  ... 

On computer-assisted classification of coupled integrable equations

Mikhail V. Foursov, Marc Moreno Maza
2001 Proceedings of the 2001 international symposium on Symbolic and algebraic computation - ISSAC '01  
We show how the triangularization method of Moreno Maza can be successfully applied to the problem of classification of homogeneous coupled integrable equations.  ...  The classifications rely on the recent algorithm developed by Foursov that requires solving 17 systems of polynomial equations.  ...  Let us first recall the results of classification of lower-order KdV-like equations. Theorem 3.1.  ... 
doi:10.1145/384101.384120 dblp:conf/issac/FoursovM01 fatcat:kh3yzx7drvdt3fsu5r4a3h36eq

On Computer-assisted Classification of Coupled Integrable Equations

Mikhail V. Foursov, Marc Moreno Maza
2002 Journal of symbolic computation  
We show how the triangularization method of Moreno Maza can be successfully applied to the problem of classification of homogeneous coupled integrable equations.  ...  The classifications rely on the recent algorithm developed by Foursov that requires solving 17 systems of polynomial equations.  ...  Let us first recall the results of classification of lower-order KdV-like equations. Theorem 3.1.  ... 
doi:10.1006/jsco.2002.0527 fatcat:6n3ocxwnjjhpdg5h46m3yx3w6q

Page 8819 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
(PRC-FUDAN-NS; Shanghai) A series of new exact solutions for a complex coupled KdV system. (English summary) Chaos Solitons Fractals 19 (2004), no. 3, 515-5235.  ...  For illustration, we apply the method proposed to revisit a complex coupled KdV system and construct successfully a series of new exact solutions including the soliton solutions and elliptic doubly periodic  ... 

Page 4435 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
the classification of seventh-order KdV-like equations admitting a formal symmetry of order 16 is completed.  ...  integrable KdV-like seventh-order equations are the KdV, Sawada-Kotera, and Kaup equations.  ... 

Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I

Takayuki Tsuchida, Thomas Wolf
2005 Journal of Physics A: Mathematical and General  
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries.  ...  Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of 2nd order systems with a 3rd order or a 4th order symmetry  ...  Acknowledgments One of the authors (TT) would like to thank Professor Junkichi Satsuma, Professor Miki Wadati, Professor Tetsuji Tokihiro and Professor Yasuhiro Ohta for their useful comments.  ... 
doi:10.1088/0305-4470/38/35/006 fatcat:bulzqvdrofgldammve5evo6ode

Euler-Poincaré Formalism of Coupled KdV Type Systems and Diffeomorphism Group on S1

P. Guha
2005 Journal of Applied Analysis  
This paper describes a wide class of coupled KdV equations. The first set of equations directly follow from the geodesic flows on the Bott-Virasoro group with a complex field.  ...  We compute the Lie-Poisson brackets of the Antonowicz-Fordy system, and the mode expansion of these beackets yield the twisted Heisenberg-Virasoro algebra.  ...  He like to thanks Dr. Ain-Ul Huda for Tex assistence.  ... 
doi:10.1515/jaa.2005.261 fatcat:e5p4huqcrbclhhwq4cgyddteuu

Analytical and Numerical Computations of Multi-Solitons in the Korteweg-de Vries (KdV) Equation

Hycienth O. Orapine, Emem Ayankop-Andi, Godwin J. Ibeh
2020 Applied Mathematics  
In this paper, an analytical and numerical computation of multi-solitons in Korteweg-de Vries (KdV) equation is presented.  ...  In the analytical computation, the multi-solitons in KdV equation are computed symbolically using computer symbolic manipulator-Wolfram Mathematica via Hirota method because of the lengthy algebraic computation  ...  Conflicts of Interest The authors declare no conflicts of interest regarding the publication of this paper.  ... 
doi:10.4236/am.2020.117037 fatcat:davvifgmqval3ig6wg3vg3mpfm

Interactions of large amplitude solitary waves in viscous fluid conduits

Nicholas K. Lowman, M. A. Hoefer, G. A. El
2014 Journal of Fluid Mechanics  
a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking.  ...  The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified  ...  Classification of interactions: KdV In the case of the KdV equation, i.e. the weakly nonlinear, long wavelength regime, properties due to integrability have been used to classify the overtaking interaction  ... 
doi:10.1017/jfm.2014.273 fatcat:7u6pq6rafbgflailh422t574fi

The Integrability of New Two-Component KdV Equation

Ziemowit Popowicz
2010 Symmetry, Integrability and Geometry: Methods and Applications  
We consider the bi-Hamiltonian representation of the two-component coupled KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich and Foursov.  ...  Connection of this equation with the supersymmetric Kadomtsev-Petviashvilli-Radul-Manin hierarchy is presented.  ...  Gürses and Karasu, in order to check the integrability of the system of equations (2) , assumed that the system is integrable if it admits a recursion operator.  ... 
doi:10.3842/sigma.2010.018 fatcat:pvypqd3rebdlrca7gpgmr6v7qq

Roland's DOI Article

Roland Pennings
2007 Journal of Non-linear Mathematical Physics  
The natural lift of the action of Dif f (S 1 ) yields Dif f (S 1 )-module. In this paper we demonstate this construction to yield several examples of dispersionless integrable systems.  ...  Finally, we study the Moyal quantization of all such systems to construct noncommutative systems. Dedicated to Professor Dieter Mayer on his 60th birthday  ...  He would like to thank Professor Miki Wadati and Dr. Ning Wang for their interests.  ... 
doi:10.2991/000002 fatcat:37ukugp4prfbtlenzffu2ghizm

Non-autonomous Degenerate KdV Systems [article]

Refik Turhan
2002 arXiv   pre-print
Non-autonomous degenerate KdV systems in (1+1) dimensions are considered for integrability classification. Integrability of the systems is associated with the existence of a recursion operator.  ...  Some new non-autonomous degenerate two-component KdV systems are found.  ...  This work is partially supported by the Scientific and Technical Research Council of Turkey (TÜBİTAK).  ... 
arXiv:nlin/0201056v1 fatcat:vkfvxxdsibc25fs62ahvu7ykwy

Symbolic Representation and Classification of N=1 Supersymmetric Evolutionary Equations

Kai Tian, Jing Ping Wang
2017 Studies in applied mathematics (Cambridge)  
all such integrable equations.  ...  We extend the symbolic representation to the ring of N = 1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Fréchet derivative and super  ...  KT would like to thank the School of Mathematics, Statistics & Actuarial Science for the hospitality.  ... 
doi:10.1111/sapm.12163 fatcat:6z4syq6lxvg5xnpelcdiplfrji
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