منابع مشابه
Hamiltonian PDEs: deformations, integrability, solutions
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 behaviour of solutions to such systems. PACS numbers: 02.30.Ik, 02.30.Jr
متن کاملBroer-Kaup-Kupershmidt Equations
and Applied Analysis 3 (2) If 0 < g < g0, we get a solitary wave solution u6 ( x, y, t ) c (√ 2 α − 1 β cosh θ ( x y − ct )) α − 1 ( 1 β − cosh 2θ ( x y − ct )) α ( −1 α β − α − 1 cosh 2θ ( x y − ct )) , 2.4 and two blow-up solutions u7± ( x, y, t ) c ( α ( 2 β ) − 2 − 2 α − 1 cosh θ ( x y − ct ) ± β 3/2 coth θ/2 ( x y − ct )) 2α ( −1 α β − α − 1 cosh θ ( x y − ct )) , 2.5 where β 6 − 6α α2 and...
متن کاملOn the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces
It is established that there exists an intimate connection between isometric deformations of polyhedral surfaces and discrete integrable systems. In particular, Sauer’s kinematic approach is adopted to show that second-order infinitesimal isometric deformations of discrete surfaces composed of planar quadrilaterals (discrete conjugate nets) are determined by the solutions of an integrable discr...
متن کاملProcrustean statistical inference of deformations
A two step method has been devised for the statistical inference of deformation changes. In the first step of this method and based on Procrustes analysis of deformation tensors, the significance of the change in a time or space series of deformation tensors is statistically analyzed. In the second step significant change(s) in deformations are localized. In other words, they are assigned to ce...
متن کاملThe Kupershmidt hydrodynamic chains and lattices
This paper is devoted to the very important class of hydrodynamic chains (see [9], [23], [24]) first derived by B. Kupershmidt in [14], later re-discovered by M. Blaszak in [4] (see also [21]). An infinite set of local Hamiltonian structures, hydrodynamic reductions parameterized by the hypergeometric function and reciprocal transformations for the Kupershmidt hydrodynamic chains are described....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2009
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-009-9442-4