Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersive shock waves in Three Dimensional Benjamin-Ono equation   Dispersive shock waves (DSWs) in the three dimensional Benjamin- Ono (3DBO)
equation is studied with step-like initial condition along a paraboloid front.
By using a similarity reduction, problem of studying DSWs in three space one
time (3+1) dimensions reduces to finding DSW solution of a (1+1) dimensional
equation. By using a special ansatz, the 3DBO equation exactly reduces to the
spherical Benjamin-Ono (sBO) equation. Whitham modulation equations are derived
which describes DSW evolution in the sBO equation by using a perturbation
method and these equations are written in terms of appropriate Riemmann type
variables to obtain the sBO- Whitham system. DSW solution which obtained from
the numerical solutions of the Whitham system and the direct numerical solution
of the sBO equation are compared. In this comparison, a good agreement is found
between these solutions. Also, some physical qualitative results about DSWs in
sBO equation are presented. It is concluded that DSW solutions in the reduced
sBO equation provide some information about DSW behaviour along the paraboloid
fronts in the 3DBO equation.

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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: math