Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions to the (1+1)-dimensional nonlinear Maxwell equations in
  the orthogonal curvilinear coordinates   Characterizing electromagnetic wave propagation in nonlinear and
inhomogeneous media is of great interest from both theoretical and practical
perspectives, even though it is extremely complicated. In fact, it is still an
unresolved issue to find the exact solutions to the nonlinear waves in the
orthogonal curvilinear coordinates. In this paper, we present an analytic
method to handle the problem of electromagnetic waves propagation in
arbitrarily nonlinear and particularly inhomogeneous media without dispersion.
Through the exact solutions of the (1+1)-dimensional nonlinear Maxwell
equations, we discuss some nonlinear phenomena, including cylindrical shock
waves, free nonlinear oscillations, and nonlinear superposition of waves.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th