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Singularities of Type-Q ABS Equations

by James Atkinson - SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS , 2011
"... The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the ..."
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The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine

Singular-boundary reductions of type-Q ABS equations

by James Atkinson, Nalini Joshi
"... We study the fully discrete elliptic integrable model Q4 and its immediate trigonomet-ric 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 trigonomet-ric 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 TYPE-Q ABS EQUATIONS

by Mike Hayn, Phil Howesr, Yang Shiq
"... 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 q-Painleve ́ 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 q-Painleve ́ equation at the top of the Painleve ́ hierarchy, existing on the same

4 GEOMETRIC REDUCTIONS OF ABS EQUATIONS ON AN n-CUBE TO DISCRETE PAINLEVE ́ SYSTEMS

by N. Joshi, N. Nakazono, Y. Shi
"... ar ..."
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Abstract not found

ABS EQUATIONS ARISING FROM DISCRETE PAINLEV ´E SYSTEMS: ω-LATTICE FOR THE (A2 + A1)(1) CASE

by Nalini Joshi, Nobutaka Nakazono, Yang Shi
"... ar ..."
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Abstract not found

On Miura Transformations and Volterra-Type Equations Associated with the Adler–Bobenko–Suris Equations

by Decio Levi, Matteo Petrera, Christian Scimiterna, Ravil Yamilov - 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 ..."
Abstract - Cited by 15 (8 self) - Add to MetaCart
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

Operator Equation AB = BA

by Bhaggy P. Duggal, Robin Harte
"... We continue the investigation of the operator equation AB = BA for normal operators on Banach space is studied, and in particular char-acterize 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 char-acterize the commutativity condition = 1. Mathematics Subject Classication: 46H99

Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations

by Yen-hsi Richard Tsai, Li-tien Cheng, Stanley Osher, Hong-kai Zhao - SIAM Journal on Numerical Analysis , 2003
"... We derive a Godunov-type 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 Gauss-Seidel type iterations for solving the corresponding Hamilton-Jacobi Equations. Th ..."
Abstract - Cited by 136 (20 self) - Add to MetaCart
We derive a Godunov-type 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 Gauss-Seidel type iterations for solving the corresponding Hamilton-Jacobi Equations

a,b ∗

by Wen-xiu Ma , 804
"... to the 2D Toda lattice equation ..."
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to the 2D Toda lattice equation

Soliton Solutions for ABS Lattice Equations

by Frank W Nijhoff, James Atkinson - I Cauchy Matrix Approach, J. Phys. A: Math. Theor
"... Abstract. Elliptic N-soliton-type 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 ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
Abstract. Elliptic N-soliton-type 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 of 1,384