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Symmetries and integrable systems. [PDF]

Fundam Res
Lou SY, Feng BF.
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SUPERSYMMETRIES AND RECURSION OPERATORS FOR $N=2$ SUPERSYMMETRIC KDV-EQUATION (Lie Groups, Geometric Structures and Differential Equations : One Hundred Years after Sophus Lie)

, 2000
P.H.M. Kersten
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A new integrable equation that combines the KdV equation with the negative‐order KdV equation

Mathematical Methods in the Applied Sciences, 2017
In this work, we develop a new integrable equation by combining the KdV equation and the negative‐order KdV equation. We use concurrently the KdV recursion operator and the inverse KdV recursion operator to construct this new integrable equation. We show that this equation nicely passes the Painlevé test.
A. Wazwaz
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Linear superposition of Wronskian rational solutions to the KdV equation

Communications in Theoretical Physics, 2021
A linear superposition is studied for Wronskian rational solutions to the KdV equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial ...
W. Ma
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Painlevé-type asymptotics of an extended modified KdV equation in transition regions

, 2021
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of an extended modified KdV equation with decaying initial data in two transition regions, completing previous results by Liu et al. in [18] .
Nan Liu, B. Guo
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KdV Equations and Integrability Detectors

Acta Applicandae Mathematicae, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grammaticos, B., Papageorgiou, V., Ramani, A.   +2 more
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VARIATIONAL PRINCIPLE FOR A GENERALIZED KdV EQUATION IN A FRACTAL SPACE

Fractals, 2020
A generalized KdV equation with fractal derivatives is suggested, and a special function is introduced to establish a fractal variational principle. A detailed derivation is elucidated step by step by the semi-inverse method, and some special cases are ...
Yue Shen, Ji-Huan He
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Soliton molecules, nonlocal symmetry and CRE method of the KdV equation with higher-order corrections

Physica Scripta, 2020
The soliton molecules of the Korteweg–de Vries (KdV) equation with higher-order corrections are studied by using the velocity resonance mechanism and the multi-soliton solution.
Bo Ren, Ji Lin
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Reduction of KdV and Cylindrical KdV Equations to Painlevé Equation

Journal of the Physical Society of Japan, 1982
Similarity solutions of the KdV and cylindrical KdV equations are studied by means of Lie's method of infinitesimal transformation groups. It is shown that the KdV equation is reduced to the Painleve transcendental equation of the first or second kind.
Masayoshi Tajiri, Shunji Kawamoto
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