Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Alfv\'en waves in extended magnetohydrodynamics   Large-amplitude Alfv\'en waves are observed in various systems in space and
laboratories, demonstrating an interesting property that the wave shapes are
stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model
predicts that an Alfv\'en wave keeps an arbitrary shape constant when it
propagates on a homogeneous ambient magnetic field. However, such arbitrariness
is an artifact of the idealized model that omits the dispersive effects. Only
special wave forms, consisting of two component sinusoidal functions, can
maintain the shape; we derive fully nonlinear Alfv\'en waves by an extended MHD
model that includes both the Hall and electron inertia effects. Interestingly,
these \small-scale effects" change the picture completely; the large-scale
component of the wave cannot be independent of the small scale component, and
the coexistence of them forbids the large scale component to have a free wave
form. This is a manifestation of the nonlinearity-dispersion interplay, which
is somewhat different from that of solitons.

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The categories of this paper are: cs
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex