[HTML][HTML] A generalized Dirac soliton hierarchy and its bi-Hamiltonian structure
Y Ye, Z Li, C Li, S Shen, WX Ma - Applied Mathematics Letters, 2016 - Elsevier
Y Ye, Z Li, C Li, S Shen, WX Ma
Applied Mathematics Letters, 2016•Elsevier… In this letter, we will present a generalized Dirac soliton hierarchy and construct its bi-Hamiltonian
structure. An important member in the hierarchy reads (1.1) { p t = − 1 2 q x x + p 2 q + q 3 − 4
α p ( p p x + q q x ) − 2 α 2 ( p 4 q + 2 p 2 q 3 + q 5 ) , q t = 1 2 p x x − p q 2 − p 3 − 4 α q ( p p x
+ q q x ) + 2 α 2 ( p q 4 + 2 p 3 q 2 + p 5 ) , where α is an arbitrary constant. Eq. (1.1) can be
reduced to the classical … In Section 2, we present a new matrix spectral problem associated
with the three-dimensional real special linear Lie algebra sl ( 2 , R ) and then construct the …
structure. An important member in the hierarchy reads (1.1) { p t = − 1 2 q x x + p 2 q + q 3 − 4
α p ( p p x + q q x ) − 2 α 2 ( p 4 q + 2 p 2 q 3 + q 5 ) , q t = 1 2 p x x − p q 2 − p 3 − 4 α q ( p p x
+ q q x ) + 2 α 2 ( p q 4 + 2 p 3 q 2 + p 5 ) , where α is an arbitrary constant. Eq. (1.1) can be
reduced to the classical … In Section 2, we present a new matrix spectral problem associated
with the three-dimensional real special linear Lie algebra sl ( 2 , R ) and then construct the …
By using symbolic computation software (Maple), a generalized Dirac soliton hierarchy is derived from a new matrix spectral problem associated with the Lie algebra sl (2, R). A bi-Hamiltonian structure yielding Liouville integrability is furnished by the trace identity.
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