1,253 research outputs found
A discrete linearizability test based on multiscale analysis
In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A1, A2 and A3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A3 C-integrability conditions can be linearized by a Möbius transformation
The matrix Kadomtsev--Petviashvili equation as a source of integrable nonlinear equations
A new integrable class of Davey--Stewartson type systems of nonlinear partial
differential equations (NPDEs) in 2+1 dimensions is derived from the matrix
Kadomtsev--Petviashvili equation by means of an asymptotically exact nonlinear
reduction method based on Fourier expansion and spatio-temporal rescaling. The
integrability by the inverse scattering method is explicitly demonstrated, by
applying the reduction technique also to the Lax pair of the starting matrix
equation and thereby obtaining the Lax pair for the new class of systems of
equations. The characteristics of the reduction method suggest that the new
systems are likely to be of applicative relevance. A reduction to a system of
two interacting complex fields is briefly described.Comment: arxiv version is already officia
Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions
It is shown that a class of important integrable nonlinear evolution
equations in (2+1) dimensions can be associated with the motion of space curves
endowed with an extra spatial variable or equivalently, moving surfaces.
Geometrical invariants then define topological conserved quantities. Underlying
evolution equations are shown to be associated with a triad of linear
equations. Our examples include Ishimori equation and Myrzakulov equations
which are shown to be geometrically equivalent to Davey-Stewartson and Zakharov
-Strachan (2+1) dimensional nonlinear Schr\"odinger equations respectively.Comment: 13 pages, RevTeX, to appear in J. Math. Phy
Max Scheler e la possibilità di una nuova forma di antispecismo
This article presents the ethical thought of Max Scheler, beyond its anthropocentric specificity, as a possible basis for the philosophical elaboration of an anti-speciesist ethical phenomenology, of Christian origin, which in turn presupposes for the self-understanding of our human existence a vegan and anti-speciesist ethical praxis, as a concrete form of active love as care for every life
Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems
The Hall--Post inequalities provide lower bounds on -body energies in
terms of -body energies with . They are rewritten and generalized to
be tested with exactly-solvable models of Calogero-Sutherland type in one and
higher dimensions. The bound for spinless fermions in one dimension is
better saturated at large coupling than for noninteracting fermions in an
oscillatorComment: 7 pages, Latex2e, 2 .eps figure
On the Integrability of the Discrete Nonlinear Schroedinger Equation
In this letter we present an analytic evidence of the non-integrability of
the discrete nonlinear Schroedinger equation, a well-known discrete evolution
equation which has been obtained in various contexts of physics and biology. We
use a reductive perturbation technique to show an obstruction to its
integrability.Comment: 4 pages, accepted in EP
Multiple-scale analysis of discrete nonlinear partial difference equations: the reduction of the lattice potential KdV
We consider multiple lattices and functions defined on them. We introduce
slow varying conditions for functions defined on the lattice and express the
variation of a function in terms of an asymptotic expansion with respect to the
slow varying lattices.
We use these results to perform the multiple--scale reduction of the lattice
potential Korteweg--de Vries equation.Comment: 17 pages. 1 figur
Necessary and sufficient conditions for existence of bound states in a central potential
We obtain, using the Birman-Schwinger method, a series of necessary
conditions for the existence of at least one bound state applicable to
arbitrary central potentials in the context of nonrelativistic quantum
mechanics. These conditions yield a monotonic series of lower limits on the
"critical" value of the strength of the potential (for which a first bound
state appears) which converges to the exact critical strength. We also obtain a
sufficient condition for the existence of bound states in a central monotonic
potential which yield an upper limit on the critical strength of the potential.Comment: 7 page
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