Integrable Quartic Potentials and Coupled KdV Equations
نویسنده
چکیده
We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the 1 : 6 : 1 integrable case quartic potential. A generalisation of the 1 : 6 : 8 case is similarly related to a different (but gauge related) fourth order Lax operator. We exploit this connection to derive a Lax representation for each of these integrable systems. In this context a canonical transformation is derived through a gauge transformation.
منابع مشابه
Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions
Auxiliary systems for matrix nonisospectral equations, including coupled NLS with external potential and KdV with variable coefficients, were introduced. Explicit solutions of nonisospectral equations were constructed using the GBDT version of the Bäcklund-Darboux transformation. PACS numbers: 02.30.Ik, 02.30Yy, 03.65.Ge
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