Results 1 to 10 of about 1,069 (170)
A Bäcklund Transformation for the Burgers Hierarchy [PDF]
Abstract and Applied Analysis, 2010 We give a Bäcklund transformation in a unified form for each member in the Burgers hierarchy. By applying the Bäcklund transformation to the trivial solutions, we generate some solutions of the Burgers hierarchy.
Xifang Cao, Chuanyou Xu
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Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations [PDF]
Journal of High Energy Physics, 2018 The integrability of the N=1 $$ \mathcal{N}=1 $$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation
A.R. Aguirre +4 more
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Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS [PDF]
Nuclear Physics B, 2017 We consider the discrete and continuous vector non-linear Schrödinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the
Panagiota Adamopoulou +2 more
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A modified Suris hierarchy and N-fold Darboux -Bäcklund transformation
Partial Differential Equations in Applied Mathematics, 2022 A modified Suris hierarchy is derived by discrete zero curvature equation. Bi-Hamiltonian structure of the whole hierarchy is established through the discrete trace identity. And we prove that the obtained hierarchy is Liouville integrable.
Ning Zhang, Xi-Xiang Xu
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Examples and Counterexamples, 2022 Herein, the Painlevé analysis and Bäcklund transformation for the (3+1) dimensional Burger equation are presented. Using this analysis, it is shown that the equation under consideration non-integrable.
M.H.M. Moussa, Zidan M. Abd Al-Halim
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A note on Bäcklund transformations for the Harry Dym equation
Partial Differential Equations in Applied Mathematics, 2022 The Bäcklund transformations are revisited for the Harry Dym equation. The associated nonlinear superposition formula, which consists of two equations — one for the field variable and the other for the spatial variable, is also presented.
Kai Tian, Mengyuan Cui, Q.P. Liu
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Mathematics, 2022 The reverse space-time nonlocal complex modified Kortewewg–de Vries (mKdV) equation is investigated by using the consistent tanh expansion (CTE) method.
Junda Peng +3 more
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Results in Physics, 2022 Of current fluid-dynamics interest, Results Phys. 41, 105937 (2022) has presented an extended time-dependent (3+1)-dimensional shallow water wave equation in an ocean or a river, with some solitons, breathers, lump waves and mixed breather-soliton ...
Xin-Yi Gao, Yong-Jiang Guo, Wen-Rui Shan
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Journal of Ocean Engineering and Science, 2023 This article considers time-dependent variable coefficients (2+1) and (3+1)-dimensional extended Sakovich equation. Painlevé analysis and auto-Bäcklund transformation methods are used to examine both the considered equations.
Shailendra Singh, S. Saha Ray
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Advances in Mathematical Physics, 2020 In this article, we mainly apply the nonlocal residual symmetry analysis to a (2 + 1)-dimensional strongly coupled Burgers system, which is defined by us through taking values in a commutative subalgebra.
Haifeng Wang, Yufeng Zhang
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