Relativistic DNLS and Kaup-Newell Hierarchy

By the recursion operator of the Kaup-Newell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit $c \rightarrow \infty$ it reduces to DNLS equation and preserves integrability at any order of relativistic corrections. The compact explicit representation of the linear problem for this equation becomes possible due to notions of the $q$-calculus with two bases, one of which is the recursion operator, and another one is the spectral parameter

イオン音波の非線形現象 : ソリトンからカオスへの遷移およびシース構造の分岐

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 吉田 善章, 東京大学教授 小川 雄一, 東京大学教授 鈴木 宏二郎, 東京大学准教授 西浦 正樹, 日本大学元教授 戸次 直明University of Tokyo(東京大学

Dissipative hierarchies and resonance solitons for KP-II and MKP-II

We show that dissipative solitons (dissipatons) of the second and the third members of SL(2,R) AKNS hierarchy give rise to the real solitons of KP-II, while for SL(2,R) Kaup-Newell hierarchy they give solitons of MKP-II. By the Hirota bilinear form for both flows, we find new bilinear system for these equations, and one- and two-soliton solutions. For special values of parameters our solutions show resonance behaviour with creation of four virtual solitons. We first time created four virtual soliton resonance solution for KP-II and established relations of it with degenerate four-soliton solution in the Hirota-Satsuma bilinear form for KP-II. Our approach allows one to interpret the resonance soliton as a composite object of two dissipative solitons in 1 + 1 dimensions.Izmir Institute of Technology and Institute of Mathematics, Academia Sinic