Results 1 to 10 of about 883 (177)
Bäcklund Transformations for Liouville Equations with Exponential Nonlinearity [PDF]
Axioms, 2021 This work aims to obtain new transformations and auto-Bäcklund transformations for generalized Liouville equations with exponential nonlinearity having a factor depending on the first derivatives.
Tatyana V. Redkina +3 more
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Classical integrable defects as quasi Bäcklund transformations [PDF]
Nuclear Physics B, 2016 We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the “equations of motion” on the defect point via the space-like and time-like description.
Anastasia Doikou
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The bäcklund transformations of the fifth painlevé equation and their applications [PDF]
Mathematical Modelling and Analysis, 2001 The main objective of this paper is to study the properties of the Bäcklund transformations and the auto‐Bäcklund transformations, to construct the nonlinear superposition formulas for the solutions of the fifth Painlevé equation and to obtain the values
V. Gromak, G. Filipuk
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Thiophene Derivatives as Versatile Precursors for (Hetero)Arene and Natural Product Synthesis. [PDF]
Angew Chem Int Ed EnglHidden but Powerful: Thiophenes and their saturated analogues have been demonstrated to be versatile C4‐building blocks that can be rapidly applied to natural product synthesis and the construction of functionalized (hetero)arenes. This minireview aims to provide a concise overview of the strategies and implementations of these sulfur‐containing ...
Keimer A, Haut FL.
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Novel Bäcklund Transformations for Integrable Equations
Mathematics, 2022 In this paper, we construct a new matrix partial differential equation having a structure and properties which mirror those of a matrix fourth Painlevé equation recently derived by the current authors.
Pilar Ruiz Gordoa, Andrew Pickering
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Painlevé Test and Exact Solutions for (1 + 1)-Dimensional Generalized Broer–Kaup Equations
Mathematics, 2022 In this paper, the Painlevé integrable property of the (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, the Bäcklund transformations for the gBK equations are derived by using the Painlevé truncation.
Sheng Zhang, Bo Xu
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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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Advances in Mathematical Physics, 2022 In this letter, we consider a new two-component system. By its reciprocal relation with the first negative flow in the AKNS hierarchy, we construct three Darboux-Bäcklund transformations for the new system and obtain some soliton-like solutions.
Shilong Huang, Hongmin Li
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BACKLUND TRANSFORMATIONS FOR LIOUVILLE’S EQUATIONS WITH EXPONENTIAL NONLINEARITY
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. The study of Backlund 's transformations is one of the current topics in the theory of differential equations in partial derivatives. Such transformations are used to find solutions to nonlinear differential equations, including solitonic ...
T. V. Red'kina, O. V. Novikova
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Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. Finding exact solutions of nonlinear partial differential equations is one of the main problems of the nonlinear systems theory. A number of methods have been developed for integrable systems, but due to the complexity of various nonlinear
T. V. Red'kina, O. V. Novikova
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