Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2005-12-16
J.Math.Phys.48:042702,2007
Nonlinear Sciences
Exactly Solvable and Integrable Systems
16 pages, LaTeX 2e, no figures (in this version the recursion operator for the Sasa--Satsuma equation was written in a somewha
Scientific paper
10.1063/1.2710552
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.
Demskoi Dmitry
Sergyeyev Artur
No associations
LandOfFree
The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries, and more does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries, and more, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries, and more will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-112452