Results 81 to 90 of about 22,025,942 (161)
Alexandria Engineering JournalThis research explores the Painlevé integrable (2+1)-dimensional Extended Kadomtsev–Petviashvili equation from different perspectives. Hirota’s bilinear form of the underlying equation has been used to obtain different exact solutions and they are then ...
Rutaba Saleem, Ahmad Javid
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, 2020 This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ...
Conte, Robert, Musette, Micheline
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Second-order fourth-degree Painlevé-type equations [PDF]
, 2001 Transformations that involve a Fuchsian-type equation are used to obtain one-to-one correspondence between the Painlevé I-IV equations and certain second-order fourth-degree Painlevé-type equations.Transformations that involve a Fuchsian-type equation ...
Sakka, A.
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, 2015 This paper begins with a brief review of the history of the Painlevé property. The Painlevé test is applied to two non linear partial differential equations (the Tu equation, and an extended m KdVequation) which have not been tested in this way before ...
Fujioka, Jorge
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, 2002 We give Bäcklund transformations for the Painlevé I and Painlevé II equations to second-order and higher degree equations of Painlevé type.We give Bäcklund transformations for the Painlevé I and Painlevé II equations to second-order and higher degree ...
Sakka, A.
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MathematicsOur study focuses on the governing equation of a finitely deformed flexible rod with strain waves. By utilizing the well-known Ablowita–Ramani–Segur (ARS) algorithm, we prove that the equation is non-integrable in the Painlevé sense.
Adel Elmandouh +2 more
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Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation
Advances in Mathematical Physics, 2019 In this paper, we focus on the Holm-Hone equation which is a fifth-order generalization of the Camassa-Holm equation. It was shown that this equation is not integrable due to the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and ...
Guo Wang +3 more
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Non-Abelian Painlevé equations
, 2023 Des extensions non abéliennes de divers systèmes intégrables constituent l'un des centres d'intérêt de la physique mathématique moderne. En raison du lien étroit entre les modèles intégrables et les équations de Painlevé, ces dernières constituent un bon
Bobrova, Irina
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Painlevé singularity structure analysis of three component Gross–Pitaevskii type equations [PDF]
, 2009 In this paper, we have studied the integrability nature of a system of three-coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painlevé singularity structure analysis ...
Wadati, M. +9 more
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Machine Learning and Knowledge ExtractionRecent work on the evaluation of large language models emphasizes that the relevant unit of intelligence is not the artificial system alone but the human–AI hybrid.
Michel Planat
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