Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solitary wave solutions of nonlinear partial differential equations
  based on the simplest equation for the function $1/\cosh^n$   The method of simplest equation is applied for obtaining exact solitary
traveling-wave solutions of nonlinear partial differential equations that
contain monomials of odd and even grade with respect to participating
derivatives. The used simplest equation is $f_\xi^2 = n^2(f^2 -f^{(2n+2)/n})$.
The developed methodology is illustrated on two examples of classes of
nonlinear partial differential equations that contain: (i) only monomials of
odd grade with respect to participating derivatives; (ii) only monomials of
even grade with respect to participating derivatives. The obtained solitary
wave solution for the case (i) contains as particular cases the solitary wave
solutions of Korteweg-deVries equation and of a version of the modified
Korteweg-deVries equation.

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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs