Trajectories of a quadratic differential related to a quasi-exactly solvable sextic oscillator

2017/12/17 by Atia, Mohamed Jalel, Karrou, Wafaa, Chouikhi, Mondher +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.06090

Abstract

In this paper, we discuss the existence of solution (as Cauchy transform of a signed measure) of a particular algebraic quadratic equation of the form C²( z) +r( z) C( z) +s( z) =0. This problem remains to describe the critical graph of a related polynomial quadratic differential; in particular, we discuss the existence of finite critical trajectories of this quadratic differential.

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