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593
The Symbolic Integration of Exact PDEs,
 J. Symb. Comp.
, 2000
"... Abstract An algorithm is described which decides if a given polynomial differential expression ∆ of multivariate functions is exact, i.e. whether there exists a first integral P such that D x P = ∆ for any one x of a set of n variables and to provide the integral P . A generalization is given to al ..."
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Cited by 10 (6 self)
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Abstract An algorithm is described which decides if a given polynomial differential expression ∆ of multivariate functions is exact, i.e. whether there exists a first integral P such that D x P = ∆ for any one x of a set of n variables and to provide the integral P . A generalization is given
On billiard solutions of nonlinear PDEs
 Phys. Lett. A
, 1999
"... This letter presents some special features of a class of integrable PDE’s admitting billiardtype solutions, which set them apart from equations whose solutions are smooth, such as the KdV equation. These billiard solutions are weak solutions that are piecewise smooth and have rst derivative discont ..."
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Cited by 2 (0 self)
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This letter presents some special features of a class of integrable PDE’s admitting billiardtype solutions, which set them apart from equations whose solutions are smooth, such as the KdV equation. These billiard solutions are weak solutions that are piecewise smooth and have rst derivative
INTEGRABLE TRILINEAR PDE’s
, 1994
"... In a recent publication we proposed an extension of Hirota’s bilinear formalism to arbitrary multilinearities. The trilinear (and higher) operators were constructed from the requirement of gauge invariance for the nonlinear equation. Here we concentrate on the trilinear case, and use singularity ana ..."
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Cited by 1 (0 self)
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analysis in order to single out equations that are likely to be integrable. New PDE’s are thus obtained, along with others already wellknown for their integrability and for which we obtain here the trilinear expression. 1.
A general framework for deriving integral preserving numerical methods for PDEs
 SIAM J. Sci. Comput
"... PDEs ..."
Fourthorder time stepping for stiff PDEs
 SIAM J. SCI. COMPUT
, 2005
"... A modification of the exponential timedifferencing fourthorder Runge–Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made ..."
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Cited by 94 (3 self)
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A modification of the exponential timedifferencing fourthorder Runge–Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison
MultiSymplectic Integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
 Phys. Lett. A
, 1999
"... The symplectic numerical integration of finitedimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of exisiting methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. ..."
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Cited by 84 (6 self)
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. The numerical integration of infinitedimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this paper, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R 2 : time plus one space dimension. The central idea
COMMUTATOR IDENTITIES ON ASSOCIATIVE ALGEBRAS AND INTEGRABILITY OF NONLINEAR PDE’S
, 2007
"... Abstract. It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to associate to such commutator identity both nonlinear eq ..."
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Cited by 2 (2 self)
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equation and its Lax pair. Thus problem of construction of new integrable pde’s reduces to construction of commutator identities on associative algebras. 1.
Hamiltonian PDEs: deformations, integrability, solutions
 J. Phys. A: Math. Theor
"... Abstract We review recent classification results on the theory of systems of nonlinear Hamiltonian partial differential equations with one spatial dimension, including a perturbative approach to the integrability theory of such systems, and discuss universality conjectures describing critical behav ..."
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Cited by 5 (0 self)
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Abstract We review recent classification results on the theory of systems of nonlinear Hamiltonian partial differential equations with one spatial dimension, including a perturbative approach to the integrability theory of such systems, and discuss universality conjectures describing critical
NOTE ON AN INTEGRAL INEQUALITY APPLICABLE IN PDEs
, 2008
"... ABSTRACT. The article presents and refines the results which were proven in [1]. We give a condition for obtaining the optimal constant of the integral inequality for the numerical analysis of a nonlinear system of PDEs. ..."
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ABSTRACT. The article presents and refines the results which were proven in [1]. We give a condition for obtaining the optimal constant of the integral inequality for the numerical analysis of a nonlinear system of PDEs.
On stabilized integration for timedependent PDEs
 Journal of Computational Physics
"... Dedicated to Professor Piet Wesseling for his numerous contributions in the ¯eld of numerical mathematics and computational °uid dynamics An integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and sti ® reaction terms implicitly. The method is ..."
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Dedicated to Professor Piet Wesseling for his numerous contributions in the ¯eld of numerical mathematics and computational °uid dynamics An integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and sti ® reaction terms implicitly. The method
Results 11  20
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593