Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Displaced phase-amplitude variables for waves on finite background   Wave amplification in nonlinear dispersive wave equations may be caused by
nonlinear focussing of waves from a certain background. In the model of
nonlinear Schr\"odinger equation we will introduce a transformation to
displaced phase-amplitude variables with respect to a background of
monochromatic waves. The potential energy in the Hamiltonian then depends
essentially on the phase. Looking as a special case to phases that are time
independent, the oscillator equation for the signal at each position becomes
autonomous, with the change of phase with position as only driving force for a
spatial evolution towards extreme waves. This is observed to be the governing
process of wave amplification in classes of already known solutions of NLS,
namely the Akhemediev-, Ma- and Peregrine-solitons. We investigate the case of
the soliton on finite background in detail in this Letter as the solution that
describes the complete spatial evolution of modulational instability from
background to extreme waves.

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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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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: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con