Abstract
The coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a 3 × 3 matrix spectral problem is derived by using two sets of the Lenard recursion gradients. Based on the characteristic polynomial of the Lax matrix for the CCIRD hierarchy, we introduce a trigonal curve K m − 2 of arithmetic genus m − 2 , from which the corresponding Baker-Akhiezer function and meromorphic functions on K m − 2 are constructed. Then, the CCIRD equations are decomposed into Dubrovin-type ordinary differential equations. Furthermore, the theory of the trigonal curve and the properties of the three kinds of Abel differentials are applied to obtain the explicit theta function representations of the Baker-Akhiezer function and the meromorphic functions. In particular, algebro-geometric solutions for the entire CCIRD hierarchy are obtained.
Highlights
It is significantly important to search for solutions of nonlinear partial differential equations of mathematical physics
It is necessary for us to study algebro-geometric constructions of the coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a 3 × 3 matrix spectral problem
The stationary CCIRD equations are decomposed into the system of Dubrovin-type ordinary differential equations
Summary
It is significantly important to search for solutions of nonlinear partial differential equations of mathematical physics. Based on the work of that, a systematic method was proposed to define the trigonal curve and develop the framework to analyse soliton equations associated with the 3 × 3 matrix spectral problems, from which the algebro-geometric solutions of some entire hierarchies are obtained [29,30,31,32,33,34]. Wang and Geng constructed algebro-geometric solutions of a new hierarchy of soliton equations associated with a 3 × 3 matrix spectral problem [30] based on the methods used in [28, 29]. The most important result of this paper is to give the explicit algebro-geometric solutions to the CCIRD hierarchy related to 3 × 3 matrix spectral problems by using the approaches used in [28,29,30], which complements the existing works in this area.
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