Remarks on quadratic bundles related to Hermitian symmetric spaces

Physics and Mathematics of Nonlinear Phenomena 2013

Valchev, Tihomir^1,2

School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dubline 8, Ireland^1

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussèe, 1784 Sofia, Bulgaria^2

关键词: Hermitian symmetric spaces;    Integrable hierarchy;    Nonlinear evolution equation;    Reflectionless potentials;    Scattering operators;    Scattering problems;    Soliton solutions;    Spectral properties;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012044/pdf
DOI  :  10.1088/1742-6596/482/1/012044

来源: IOP

【 摘 要 】

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)×U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.