Results 1 to 10 of about 24,955,494 (69)
A novel symmetry constraint of the super cKdV system [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 A new (1+1)-dimensional integrable system, i. e. the super coupled Korteweg-de Vries (cKdV) system, has been constructed by a super extension of the well-known (1+1)-dimensional cKdV system. For this new system, a novel symmetry constraint between the potential and eigenfunction can be obtained by means of the binary nonlinearization of its Lax pairs ...
Yu, Jing +3 more
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Nonlocal Symmetry, Painlevé Integrable and Interaction Solutions for CKdV Equations
Symmetry, 2021 In this paper, we provide a method to construct nonlocal symmetry of nonlinear partial differential equation (PDE), and apply it to the CKdV (CKdV) equations.
Yarong Xia, Ruoxia Yao, Xiangpeng Xin
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Exploring fractional-order new coupled Korteweg-de Vries system via improved Adomian decomposition method. [PDF]
PLoS OneThis paper aims to extend the applications of the projected fractional improved Adomian Decomposition method (fIADM) to the fractional order new coupled Korteweg-de Vries (cKdV) system.
Arshad M +4 more
europepmc +3 more sources
International Journal of Applied and Computational Mathematics, 2023 In this research work, two mathematical models, the (1+1)-dimensional cKdV–mKdV equation and the sinh-Gordon (shG) equation, are studied using an analytical method to obtain solitary wave solutions.
Kamruzzaman Khan +2 more
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Alternative solitons in the Hirota–Satsuma system via the direct method
Partial Differential Equations in Applied Mathematics, 2021 Multisolitons and multi-hump solitons are constructed for the coupled Korteweg–de Vries (cKdV) system introduced by Hirota and Satsuma (1981) in the context of the propagation of two waves interacting with different dispersion relations.
Hugo PARRA Prado, Luis A Cisneros-Ake
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Applied Mathematics in Science and EngineeringIn this study, time-fractional coupled Korteweg–de Vries (cKdV) equations are solved using an efficient and reliable numerical technique. The classical cKdV system has been generalized into the time-fractional cKdV system.
Awatif Muflih Alqahtani +1 more
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Stationary coupled KdV systems and their Stäckel representations [PDF]
Studies in applied mathematics (Cambridge), 2023 In this article, we investigate stationary coupled Korteweg–de Vries (cKdV) systems and prove that every N$N$-field stationary cKdV system can be written, after a careful reparameterization of jet variables, as a classical separable Stäckel system in N+1$
Marciniak, Krzysztof, +5 more
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Homotopic Approximate Solutions for the Perturbed CKdV Equation with Variable Coefficients [PDF]
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in ...
Dianchen Lu +4 more
wiley +2 more sources
Hierarchies of the Korteweg–de Vries Equation Related to Complex Expansion and Perturbation
Axioms, 2023 We consider the possibility of constructing a hierarchy of the complex extension of the Korteweg–de Vries equation (cKdV), which under the assumption that the function is real passes into the KdV hierarchy.
Tatyana V. Redkina +3 more
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Exact explicit nonlinear wave solutions to a modified cKdV equation
AIMS Mathematics, 2020 In this paper, we study nonlinear wave solutions to a modified cKdV equation by exploiting Bifurcation method of Hamiltonian systems. We identify all possible bifurcation conditions and obtain the phase portraits of the system in different regions of the
Zhenshu Wen
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