Transformations of Darboux Integrable Systems
, 2009 This article reviews some recent theoretical results about the structure of Darboux integrable differential systems and their relationship with symmetry reduction of exterior differential systems. The symmetry reduction representation of Darboux integrable equations is then used to derive some new and unusual transformations.
Anderson, Ian M., Fels, Mark E.
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SYMMETRIES AND LAX INTEGRABILITY OF THE GENERALIZED PROUDMAN-JOHNSON EQUATION
Научный вестник МГТУ ГА, 2017 We study local symmetries of the generalized Proudman-Johnson equation. Symmetries of a partial differential equation may be used to find its invariant solutions.
O. I. Morozov
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Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation. [PDF]
Sci Rep, 2023 Fan C, Li L, Yu F.
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Integral transformation and Darboux transformation
, 2009 We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux-Crum transformation. We also consider conservation of monodromy with respect to the transformations.
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Involutive sweeping surfaces with Frenet frame in Euclidean 3-space. [PDF]
Heliyon, 2023 Köseoğlu G, Bilici M.
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Coexistence of chaotic attractor and unstable limit cycles in a 3D dynamical system. [PDF]
Open Res Eur, 2021 Constantinescu D, Tigan G, Zhang X.
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Liouville Integrability in a Four-Dimensional Model of the Visual Cortex. [PDF]
J Imaging, 2021 Galyaev I, Mashtakov A.
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Periodic, n-soliton and variable separation solutions for an extended (3+1)-dimensional KP-Boussinesq equation. [PDF]
Sci Rep, 2023 Shao C +5 more
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From Quantum Curves to Topological String Partition Functions. [PDF]
Commun Math Phys, 2023 Coman I, Pomoni E, Teschner J.
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Simple Equations Method (SEsM): An Effective Algorithm for Obtaining Exact Solutions of Nonlinear Differential Equations. [PDF]
Entropy (Basel), 2022 Vitanov NK.
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