The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries, and more
| dc.creator | Sergyeyev, Artur | |
| dc.creator | Demskoi, Dmitry | |
| dc.date | 2005-12-16 | |
| dc.date | 2007-02-26 | |
| dc.date.accessioned | 2026-07-07T10:38:20Z | |
| dc.date.available | 2026-07-07T10:38:20Z | |
| dc.description | We found a new symplectic structure and a recursion operator for the Sasa--Satsuma equation widely used in nonlinear optics, $$ p_t=p_{xxx}+6 p q p_x+3 p (p q)_x,\quad q_t=q_{xxx}+6 p q q_x+3 q (p q)_x, $$ along with an integro-differential substitution linking this system to a third-order generalized symmetry of the complex sine-Gordon II system $$ u_{xy}=\frac{v u_x u_y}{u v + c} + (2 u v + c)(u v + c) k u,\qquad v_{xy}=\frac{u v_x v_y}{u v + c} + (2 u v + c)(u v + c) k v, $$ where $c$ and $k$ are arbitrary constants. Combining these two results yields a highly nonlocal hereditary recursion operator and higher Hamiltonian structures for the complex sine-Gordon II system. We also show that both the Sasa--Satsuma equation and the third order evolutionary symmetry flow for the complex sine-Gordon II system are bihamiltonian systems, and construct several hierarchies of local and nonlocal symmetries for these systems. | |
| dc.description | 16 pages, LaTeX 2e, no figures (in this version the recursion operator for the Sasa--Satsuma equation was written in a somewhat different form, several typos were fixed, and titles of the papers were added in the bibliography) | |
| dc.identifier | https://arxiv.org/abs/nlin/0512042 | |
| dc.identifier | http://arxiv.org/abs/nlin/0512042 | |
| dc.identifier | J.Math.Phys.48:042702,2007 | |
| dc.identifier | doi:10.1063/1.2710552 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/180687 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries, and more | |
| dc.type | text |