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Rational General Solutions of Trivariate Rational Differential Systems
Mathematics in Computer Science, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rational Solutions for the Fokas System
Communications in Theoretical Physics, 2015Summary: Fokas system is the simplest \((2+1)\)-dimensional extension of the nonlinear Schrödinger equation [\textit{A. S. Fokas}, Inverse Probl. 10, No. 2, L\,19-L\,22 (1994; Zbl 0804.35124), see Eq. (2)]. By using the bilinear transformation method, general rational solutions for the Fokas system are given explicitly in terms of two order-\(N ...
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Rational Solutions of Painlevé Equations
Canadian Journal of Mathematics, 2002AbstractConsider the sixth Painlevé equation (P6) below where α, β, γ and δ are complex parameters. We prove the necessary and sufficient conditions for the existence of rational solutions of equation (P6) in term of special relations among the parameters. The number of distinct rational solutions in each case is exactly one or two or infinite.
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Rational Approximation of the Rough Heston Solution
SSRN Electronic Journal, 2018Pricing in the rough Heston model of Jaisson & M. Rosenbaum [(2016) Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, The Annals of Applied Probability 26 (5), 2860–2882] requires the solution of a fractional Riccati differential equation, which is not known in explicit form.
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