Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie symmetry analysis and new periodic solitary wave solutions of
  (3+1)-dimensional generalized shallow water wave equation   Many important physical situations such as fluid flows, marine environment,
solid-state physics and plasma physics have been represented by shallow water
wave equation. In this article, we construct new solitary wave solutions for
the (3+1)-dimensional generalized shallow water wave (GSWW) equation by using
Lie symmetry method. A variety of analytic (closed-form) solutions such as new
periodic solitary wave, cross-kink soliton and doubly periodic breather-type
solutions have been obtained by using invariance of the concerned
(3+1)-dimensional GSWW equation under one-parameter Lie group of
transformations. Lie symmetry transformations have applied to generate the
different forms of invariant solutions of the (3+1)-dimensional GSWW equation.
For different Lie algebra, Lie symmetry method reduces (3+1)-dimensional GSWW
equation into various ordinary differential equations (ODEs) while one of the
Lie algebra, it is transformed into the well known (2+1)-dimensional BLMP
equation. It is affirmed that the proposed techniques are convenient, genuine
and powerful tools to find the exact solutions of nonlinear partial
differential equations (PDEs). Under the suitable choices of arbitrary
functions and parameters, 2D, 3D and contour graphics to the obtained results
of GSWW equation are also analyzed graphically.

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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: gr-qc