Bäcklund Transformation for the BC-Type Toda Lattice [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We study an integrable case of $n$-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Bäcklund transformation and prove its basic properties: canonicity, commutativity and spectrality.
Vadim Kuznetsov, Evgeny Sklyanin
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A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation [PDF]
Discrete Dynamics in Nature and Society, 2018 An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established.
Xi-Xiang Xu, Meng Xu
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The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source [PDF]
Discrete Dynamics in Nature and Society, 2012 The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property.
Yali Shen, Fengqin Zhang, Xiaomei Feng
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Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission [PDF]
Alexandria Engineering JournalGraphene has appeared as one of the most promising nanomaterials with unique thermal, electronic and mechanical properties which make it suitable for many applications in materials science, energy storage, electronics, water filtration and medicine.
Mahmoud Gaballah, Rehab M. El-Shiekh
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Bäcklund Transformation of Fractional Riccati Equation and Infinite Sequence Solutions of Nonlinear Fractional PDEs [PDF]
Abstract and Applied Analysis, 2014 The Bäcklund transformation of fractional Riccati equation with nonlinear superposition principle of solutions is employed to establish the infinite sequence solutions of nonlinear fractional partial differential equations in the sense of modified ...
Bin Lu
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Nonlocal Symmetry and Bäcklund Transformation of a Negative-Order Korteweg–de Vries Equation [PDF]
Complexity, 2019 The residual symmetry of a negative-order Korteweg–de Vries (nKdV) equation is derived through its Lax pair. Such residual symmetry can be localized, and the original nKdV equation is extended into an enlarged system by introducing four new variables. By
Jinxi Fei, Weiping Cao, Zhengyi Ma
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Bäcklund Transformation and Quasi-Periodic Solutions for a Variable-Coefficient Integrable Equation [PDF]
Abstract and Applied Analysis, 2014 Binary Bell polynomials are applied to construct bilinear formalism, bilinear Bäcklund transformation, Lax pair, and infinite conservation laws of the generalized variable-coefficient fifth-order Korteweg-de Vries equation.
Wenjuan Rui, Yufeng Zhang
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Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 A GBDT version of the Bäcklund-Darboux transformation is constructed for a non-isospectral canonical system, which plays essential role in the theory of random matrix models. The corresponding Riemann-Hilbert problem is treated and some explicit formulas
Alexander Sakhnovich
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Bäcklund Transformations for the Trigonometric Gaudin Magnet [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We construct a Bäcklund transformation for the trigonometric classical Gaudin magnet starting from the Lax representation of the model. The Darboux dressing matrix obtained depends just on one set of variables because of the so-called spectrality ...
Federico Zullo, Orlando Ragnisco
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A New Auto-Bäcklund Transformation of the KdV Equation with General Variable Coefficients and Its Application [PDF]
Abstract and Applied Analysis, 2014 First, by improving some key steps in the homogeneous balance method, a new auto-Bäcklund transformation (BT) to the KdV equation with general variable coefficients is derived.
Chunping Liu
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