Abstract
Abstract An efficient, straightforward method for obtaining multi-component integrable hierarchy and the multi-component integrable couplings system is proposed in this paper. A new 4M dimensional loop algebra X ∼ is constructed firstly, whose commutation operations defined by us are as simple and straightforward as that in the loop algebra A 1 ∼ . As an application example, a new isospectral problem is established, then the well-known multi-component Schrodinger hierarchy and the multi-component mKdV hierarchy are obtained. So we call it the multi-component S-mKdV hierarchy. Finally, an expanding loop algebra F ∼ M of the loop algebra X ∼ is presented. Based on the F ∼ M , the multi-component integrable couplings system of the multi-component S-mKdV hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach in this paper.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
