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Singularities of TypeQ ABS Equations
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2011
"... The typeQ equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdVtype integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the ..."
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The typeQ equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdVtype integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine
Singularboundary reductions of typeQ ABS equations
"... We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity analysis. We introduce a technique to obtain solutions of such p ..."
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We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity analysis. We introduce a technique to obtain solutions
A SYSTEMATIC APPROACH TO REDUCTIONS OF TYPEQ ABS EQUATIONS
"... Abstract. We present a class of reductions of Möbius type for the lattice equations known as Q1, Q2, and Q3 from the ABS list. The deautonomised form of one particular reduction of Q3 is shown to be related to the qPainleve ́ equation at the top of the Painleve ́ hierarchy, existing on the same ra ..."
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Abstract. We present a class of reductions of Möbius type for the lattice equations known as Q1, Q2, and Q3 from the ABS list. The deautonomised form of one particular reduction of Q3 is shown to be related to the qPainleve ́ equation at the top of the Painleve ́ hierarchy, existing on the same
ABS EQUATIONS ARISING FROM DISCRETE PAINLEV ´E SYSTEMS: ωLATTICE FOR THE (A2 + A1)(1) CASE
"... ar ..."
On Miura Transformations and VolterraType 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 Volterratype 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 Volterratype equations. We show that the ABS equations correspond to Bäcklund
Operator Equation AB = BA
"... We continue the investigation of the operator equation AB = BA for normal operators on Banach space is studied, and in particular characterize the commutativity condition = 1. Mathematics Subject Classication: 46H99 ..."
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We continue the investigation of the operator equation AB = BA for normal operators on Banach space is studied, and in particular characterize the commutativity condition = 1. Mathematics Subject Classication: 46H99
Fast Sweeping Algorithms for a Class of HamiltonJacobi Equations
 SIAM Journal on Numerical Analysis
, 2003
"... We derive a Godunovtype numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p, q) = � ap 2 + bq 2 − 2cpq, c 2 < ab. We combine our Godunov numerical fluxes with simple GaussSeidel type iterations for solving the corresponding HamiltonJacobi Equations. Th ..."
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Cited by 136 (20 self)
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We derive a Godunovtype numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p, q) = � ap 2 + bq 2 − 2cpq, c 2 < ab. We combine our Godunov numerical fluxes with simple GaussSeidel type iterations for solving the corresponding HamiltonJacobi Equations
Soliton Solutions for ABS Lattice Equations
 I Cauchy Matrix Approach, J. Phys. A: Math. Theor
"... Abstract. Elliptic Nsolitontype solutions, i.e. solutions emerging from the application of N consecutive Bäcklund transformations to an elliptic seed solution, are constructed for all equations in the ABS list of quadrilateral lattice equations, except for the case of the Q4 equation which is trea ..."
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Cited by 2 (1 self)
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Abstract. Elliptic Nsolitontype solutions, i.e. solutions emerging from the application of N consecutive Bäcklund transformations to an elliptic seed solution, are constructed for all equations in the ABS list of quadrilateral lattice equations, except for the case of the Q4 equation which
Results 1  10
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1,384