Nevanlinna Theory for Finding Meromorphic Solutions of Cubic-Quintic Ginzburg–Landau Equation Arising in Nonlinear Dynamics
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Research on meromorphic solution of complex differential equations using Nevanlinna theory has become a subject of great interest. This paper is devoted to finding meromorphic solutions of the cubic-quintic Ginzburg–Landau equation which arises in problems of dynamics, especially fluid dynamics. We consider the complex differential equation corresponding to cubic-quintic Ginzburg–Landau equation with coefficients being small functions of meromorphic functions. The problem has been mainly studied under the condition that meromorphic function and its first derivative share one value of the type counting multiplicity or ignoring multiplicity.
KeywordsComplex differential equations Ginzburg–Landau equation Meromorphic functions Nevanlinna theory
The author thanks the referees for useful comments that improved the paper.
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