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593
Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and GromovWitten invariants
, 2001
"... We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov Witten invariants of all genera into the theory of integrable systems. The project is focused at describing normal forms of the PDEs and their ..."
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Cited by 93 (2 self)
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We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov Witten invariants of all genera into the theory of integrable systems. The project is focused at describing normal forms of the PDEs
The RiemannHilbert Formalism For Certain Linear and Nonlinear Integrable PDEs
, 2007
"... We show that by deforming the RiemannHilbert (RH) formalism associated with certain linear PDEs and using the socalled dressing method, it is possible to derive in an algorithmic way nonlinear integrable versions of these equations. In the usual Dressing Method, one first postulates a matrix RH pr ..."
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We show that by deforming the RiemannHilbert (RH) formalism associated with certain linear PDEs and using the socalled dressing method, it is possible to derive in an algorithmic way nonlinear integrable versions of these equations. In the usual Dressing Method, one first postulates a matrix RH
Boundary value problems for linear elliptic and integrable PDEs: theory and computation
, 2012
"... initial value problem for a class of integrable equations ..."
The Geometry of Peaked Solitons and Billiard Solutions of a Class of Integrable PDE’s ∗
"... The purpose of this letter is to investigate the geometry of new classes of solitonlike solutions for integrable nonlinear equations. One example is the class of peakons introduced by Camassa and Holm [1993] for a shallow water equation. We put this equation in the framework of complex integrable Ha ..."
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The purpose of this letter is to investigate the geometry of new classes of solitonlike solutions for integrable nonlinear equations. One example is the class of peakons introduced by Camassa and Holm [1993] for a shallow water equation. We put this equation in the framework of complex integrable
A hierarchy of integrable PDEs in 2+1 dimensions associated with 2  dimensional vector fields
, 2006
"... We study a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2 dimensional vector fields, and we construct the formal solution of the associated Cauchy problems using the Inverse Scattering Transform for oneparameter families of vector field ..."
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Cited by 20 (3 self)
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We study a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2 dimensional vector fields, and we construct the formal solution of the associated Cauchy problems using the Inverse Scattering Transform for oneparameter families of vector
THE PROFINITE DIMENSIONAL MANIFOLD STRUCTURE OF FORMAL SOLUTION SPACES OF FORMALLY INTEGRABLE PDE’S
"... ar ..."
Nonlinear Evolution Equations and Dynamical Systems
, 2009
"... Integrable PDEs arising as commutation of vector ..."
Initial Data Solution at �x,t� Direct Scattering Inverse Scattering Scattering Data Time Evolution Updated Scattering DataIntegrable PDEs
"... • This work is in collaboration with my advisor, Bernard Deconinck, and Sheehan ..."
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• This work is in collaboration with my advisor, Bernard Deconinck, and Sheehan
ImplicitExplicit Methods For TimeDependent PDEs
 SIAM J. NUMER. ANAL
, 1997
"... Implicitexplicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusionconvection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection ..."
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Cited by 178 (6 self)
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Implicitexplicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusionconvection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used
Multisymplectic geometry, variational integrators, and nonlinear PDEs
 Comm. Math. Phys
, 1998
"... Abstract: This paper presents a geometricvariational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the v ..."
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Cited by 126 (24 self)
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have these important preservation properties, then follow by choosing a discrete action functional. In the case of mechanics, we recover the variational symplectic integrators of Veselov type, while for PDEs we obtain covariant spacetime integrators which conserve the corresponding discrete
Results 1  10
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593