The Sasa–Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries and more
نویسنده
چکیده
We found a new symplectic structure and a recursion operator for the Sasa–Satsuma (complex mKdV II) equation widely used in nonlinear optics, pt = pxxx + 6pqpx + 3p(pq)x, qt = qxxx + 6pqqx + 3q(pq)x, along with an integro-differential substitution linking this system to a third-order generalized symmetry of the complex sine-Gordon II system uxy = vuxuy uv + c + (2uv + c)(uv + c)ku, vxy = uvxvy uv + c + (2uv + c)(uv + c)kv, where c and k are arbitrary constants. Combining these two results yields a highly nonlocal hereditary recursion operator 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. ∗On leave from Orel State University, Russia
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