Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
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905 articles
Ahmed Fitouhi, Kamel Brahim
Pages: 324 - 340
In this paper we attempt to establish some tauberian theorems in quantum calculus. This constitutes the beginning of the study of the q-analogue of analytic theory of numbers which is the aim of a forthcoming paper.
Mauricio ANGEL, Jaime CAMACARO, Rafael D ́IAZ
Pages: 548 - 569
Deformations of the 3-differential of 3-differential graded algebras are controlled by the (3, N ) Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in that equation, introduce new geometric examples of N -differential graded algebras, and use these results to study...
David Henry
Pages: 87 - 95
We present a simple approach showing that Gerstner’s flow is dynamically possible: each particle moves on a circle, but the particles never collide and fill out the entire region below the surface wave.
Gregorio Falqui, Giovanni Ortenzi
Pages: 310 - 322
We discuss how the Camassa-Holm hierarchy can be framed within the geometry of the Sato Grassmannian. We discuss the geometry of an extension of the negative flows of the CH hierarchy, recover the well-known CH equations, and frame the problem within the theory of pseudo-differential operators.
Anestis Fotiadis
Pages: 176 - 184
We describe the problem of finding a harmonic map between noncompact manifold. Given some sufficient conditions on the domain, the target and the initial map, we prove the existence of a harmonic map that deforms the given map.
Runliang Lin, Xiaojun Liu, Yunbo Zeng
Pages: 333 - 347
A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy...
Roelof K. Brouwer
Pages: 69 - 82
The proposed relational fuzzy clustering method, called FRFP ( fuzzy relational fixed point), is based on determining a fixed point of a function of the desired membership matrix. The ethod is compared to other relational clustering methods. Simulations show the method to be very effective and less...
Joseph BERNSTEIN, Ossip SCHWARZMAN
Pages: 323 - 351
We prove that, for the irreducible complex crystallographic Coxeter group W, the following conditions are equivalent: a) W is generated by reflections; b) the analytic variety X/W is isomorphic to a weighted projective space. The result is of interest, for example, in application to topological conformal...
Hailiang LIU
Pages: 441 - 466
The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which...
Zoran GRUJIC, Henrik KALISCH
Pages: 62 - 71
The derivative nonlinear Schrödinger equation is shown to be locally well-posed in a class of functions analytic on a strip around the real axis. The main feature of the result is that the width of the strip does not shrink in time. To overcome the derivative loss, Kato-type smoothing results and...
Atsushi NAKAMULA
Pages: 152 - 163
It is known that many integrable systems can be reduced from self-dual Yang-Mills equations. The formal solution space to the self-dual Yang-Mills equations is given by the so called ADHM construction, in which the solution space are graded by vector spaces with dimensionality concerning topological...