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138
Generalised Miura Transformation
, 1994
"... Coupled KdV equations are deduced by considering the homogeneous manifold cor-responding to the homogeneous Heisenberg subalgebra of the Loop group (L(S1, SL(2, C)). Utilisation of Birkhoff decomposition and further subalgebra considera-tion leads to a new generalised form of Miura map and two sets ..."
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of modified equations. A second set of Miura transformation can also be generated leading to complicated form of coupled integrable systems. 1
On the generalized Miura transformation
, 1993
"... By generalizing the Miura transformation for WN to other classical W algebras obtained by hamiltonian reduction, we find realisations of these algebras in terms of relatively simple non-abelian current algebras, e.g. ̂ sl(2) × û(1)N, generalizing the free field realisation of WN. As an example, we ..."
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Cited by 2 (0 self)
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By generalizing the Miura transformation for WN to other classical W algebras obtained by hamiltonian reduction, we find realisations of these algebras in terms of relatively simple non-abelian current algebras, e.g. ̂ sl(2) × û(1)N, generalizing the free field realisation of WN. As an example, we
THE COLE-HOPF AND MIURA TRANSFORMATIONS REVISITED
, 1998
"... Abstract. An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura’s transformation connecting the KdV and mKdV equations is studied in detail. 1. ..."
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Cited by 1 (0 self)
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Abstract. An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura’s transformation connecting the KdV and mKdV equations is studied in detail. 1.
NOTES ON WGLn-ALGEBRAS AND QUANTUM MIURA TRANSFORMATION.
, 1993
"... We start from the quantum Miura transformation [7] for the W-algebra associated with GL(n) group and find an evident formula for quantum L-operator as well as for the action of Wl currents (l=1,..,n) on elements of the completely degenerated n-dimensional representation. Quantum formulae are obtaine ..."
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We start from the quantum Miura transformation [7] for the W-algebra associated with GL(n) group and find an evident formula for quantum L-operator as well as for the action of Wl currents (l=1,..,n) on elements of the completely degenerated n-dimensional representation. Quantum formulae
q-alg/9508003 TODA FIELDS ON RIEMANN SURFACES: REMARKS ON THE MIURA TRANSFORMATION
, 1995
"... Abstract. We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of W–algebras are thus interpreted as partial connections associated to the foliatio ..."
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Abstract. We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of W–algebras are thus interpreted as partial connections associated
On Miura Transformations and Volterra-Type Equations Associated with the Adler–Bobenko–Suris Equations
- SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2008
"... We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler–Bobenko–Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund ..."
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Cited by 15 (8 self)
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We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler–Bobenko–Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund
REGULAR SOLUTION AND LATTICE MIURA TRANSFORMATION OF BIGRADED TODA HIERARCHY*
"... Abstract. In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hierarchy(BTH). As an specific example of exponential solutions of the BTH, we consider a regular solution for the (1, 2)-BTH with 3 × 3-sized Lax matrix, and discuss some geometric structure of the soluti ..."
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of the solution from which the difference between (1, 2)-BTH and original Toda hier-archy is shown. After this, we construct another kind of Lax representation of (N, 1)-bigraded Toda hierarchy((N, 1)-BTH) which does not use the fractional operator of Lax operator. Then we introduce lattice Miura transformation
Results 1 - 10
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138
