Results 1  10
of
16
Higher Order Terms in Multiscale Expansions: A Linearized KdV Hierarchy
, 2001
"... We consider a wide class of model equations, able to describe wave propagation in dispersive nonlinear media. The Kortewegde Vries (KdV) equation is derived in this general frame under some conditions, the physical meanings of which are clarified. It is obtained as usual at leading order in some mu ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
We consider a wide class of model equations, able to describe wave propagation in dispersive nonlinear media. The Kortewegde Vries (KdV) equation is derived in this general frame under some conditions, the physical meanings of which are clarified. It is obtained as usual at leading order in some multiscale expansion. The higher order terms in this expansion are studied making use of a multitime formalism and imposing the condition that the main term satisfies the whole KdV hierarchy. The evolution of the higher order terms with respect to the higher order time variables can be described through the introduction of a linearized KdV hierarchy. This allows one to give an expression of the higher order time derivatives that appear in the right hand member of the perturbative expansion equations, to show that overall the higher order terms do not produce any secularity and to prove that the formal expansion contains only bounded terms. 1
Classification of Fully Nonlinear Integrable Evolution Equations of Third Order
, 2005
"... A fully nonlinear family of evolution equations is classified. Nine new integrable equations are found, and all of them admit a differential substitution into the Kortewegde Vries or KricheverNovikov equations. One of the equations contains hyperelliptic functions, but it is transformable into th ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
A fully nonlinear family of evolution equations is classified. Nine new integrable equations are found, and all of them admit a differential substitution into the Kortewegde Vries or KricheverNovikov equations. One of the equations contains hyperelliptic functions, but it is transformable into the KricheverNovikov equation by a differential substitution that only involves elliptic functions. 1
NonLocalized Solutions of the KadomtsevPetviashvili Equation
, 2001
"... We construct nonlocalized, real global solutions of the KadomtsevPetviashviliI equation which vanish for x → − ∞ and study their large time asymptotic behavior. We prove that such solutions eject (for t→∞) a train of curved asymptotic solitons which move behind the basic wave packet. 1 ..."
Abstract
 Add to MetaCart
(Show Context)
We construct nonlocalized, real global solutions of the KadomtsevPetviashviliI equation which vanish for x → − ∞ and study their large time asymptotic behavior. We prove that such solutions eject (for t→∞) a train of curved asymptotic solitons which move behind the basic wave packet. 1
Soliton Asymptotics of Rear Part of NonLocalized Solutions of the KadomtsevPetviashvili Equation
, 2001
"... We construct nonlocalized, real global solutions of the KadomtsevPetviashviliI equation which vanish for x → − ∞ and study their large time asymptotic behavior. We prove that such solutions eject (for t → ∞) a train of curved asymptotic solitons which move behind the basic wave packet. 1 ..."
Abstract
 Add to MetaCart
(Show Context)
We construct nonlocalized, real global solutions of the KadomtsevPetviashviliI equation which vanish for x → − ∞ and study their large time asymptotic behavior. We prove that such solutions eject (for t → ∞) a train of curved asymptotic solitons which move behind the basic wave packet. 1
Journal of Nonlinear Mathematical Physics 2001, V.8, Supplement, 6268 Proceedings: NEEDS'99 On Huygens' Principle for Dirac Operators
"... We exhibit a class of Dirac operators that possess Huygens' property, i.e., the support of their fundamental solutions is precisely the light cone. This class is obtained by considering the rational solutions of the modified Kortewegde Vries hierarchy. ..."
Abstract
 Add to MetaCart
We exhibit a class of Dirac operators that possess Huygens' property, i.e., the support of their fundamental solutions is precisely the light cone. This class is obtained by considering the rational solutions of the modified Kortewegde Vries hierarchy.