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Symmetries of Partial Differential Equations
 J. KOREAN MATH. SOC.
, 2003
"... We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C n. Using the recent developments of CauchyRiemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we d ..."
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Cited by 7 (4 self)
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We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C n. Using the recent developments of CauchyRiemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we
Symbolic . . . Systems of Nonlinear Evolution Equations
, 1997
"... A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program condens.m automatically carries out the lengthy symbolic computations for the construction of conserved d ..."
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A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program condens.m automatically carries out the lengthy symbolic computations for the construction of conserved
Symbolic methods to construct exact solutions of nonlinear partial differential equations
 MATH. COMP. IN SIMUL
, 1997
"... Two straightforward methods for finding solitarywave and soliton solutions are presented and applied to a variety of nonlinear partial differential equations. The rst method is a simplified version of Hirota's method. It is shown to be an effective tool to explicitly construct multisoliton so ..."
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Cited by 17 (1 self)
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Two straightforward methods for finding solitarywave and soliton solutions are presented and applied to a variety of nonlinear partial differential equations. The rst method is a simplified version of Hirota's method. It is shown to be an effective tool to explicitly construct multi
Invariants and symmetries for partial differential equations and lattices
 in: Proc. Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation
, 1998
"... Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as Mathematica. Invariants and symmetries are shown for several wellkno ..."
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Cited by 1 (1 self)
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Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as Mathematica. Invariants and symmetries are shown for several well
Integrated SymbolicNumeric Computing in //ELLPACK: Experiences and Plans
, 1992
"... In this paper we describe the use of integrated symbolicnumeric computing techniques in the evolving //ELLPACK 1 [HRC + 90] Problem Solving Environment. //ELLPACK is a problem solving environment (PSE) for solving partial differential equations (PDEs) using parallel architectures. It was origi ..."
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Cited by 2 (1 self)
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In this paper we describe the use of integrated symbolicnumeric computing techniques in the evolving //ELLPACK 1 [HRC + 90] Problem Solving Environment. //ELLPACK is a problem solving environment (PSE) for solving partial differential equations (PDEs) using parallel architectures
Algorithmic Integrability Tests for Nonlinear Differential and Lattice Equations
 Computer Physics Communications
, 1999
"... Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differentialdifference equations are presented. The first algorithm is the wellknown Painlev e test, which is applicable to polynomial systems of ordinary and partial differential equations. T ..."
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Cited by 16 (12 self)
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Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differentialdifference equations are presented. The first algorithm is the wellknown Painlev e test, which is applicable to polynomial systems of ordinary and partial differential equations
Calculation of beam structures with the symbolic computer language Maple
"... Beside the standard calculation programs for civil engineering buildings mathematical programs have been lately established for the solution of differential equations for the analysis of mechanical and static systems. Programs like Maple, Matlab, MathCAD and Mathematica are popular in this field. To ..."
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. To the knowledge of the authors, the widest application functionality offers the program Maple. Its advantages are, e.g. the alternatively symbolic or numerical solution of differential equation systems, the easy handling of parameter studies, the immediate visualization of results, the definition of macros
Differential Equations
, 2013
"... This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. Stateoftheart methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional l ..."
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This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. Stateoftheart methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional
Pseudospectral Symbolic Computation For Financial Models
, 1999
"... The modelling of financial markets as continuous stochastic processes provides the means to analyse the implications of models and to compute prices for a host of financial instruments. We code as a symbolic computing program the analysis, initiated by Black, Scholes and Merton, of the formation of ..."
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of a partial differential equation whose solution is the value of a derivative security, from the specification of an undelying security’s process. The Pseudospectral method is a high order solution method for partial differential equations that approximates the solution by global basis funcations. We
The structure of Lie algebras and the classification problem for partial differential equations
, 2000
"... The present paper solves completely the problem of the group classification of nonlinear heatconductivity equations of the form u t = F (t, x, u, u x )u xx + G(t, x, u, u x ). We have proved, in particular, that the above class contains no nonlinear equations whose invariance algebra has dimensi ..."
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Cited by 47 (10 self)
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, and compute the corresponding maximal symmetry algebras. The list of invariant equations obtained in this way contains (up to a local change of variables) all the previouslyknown invariant evolution equations belonging to the class of partial di#erential equations under study.
Results 11  20
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