Exploring the Chavy–Waddy–Kolokolnikov Model: Analytical Study via Recently Developed Techniques
Journal of Mathematics, Volume 2026, Issue 1, 2026.This work explores the analytical soliton solutions to the Chavy–Waddy–Kolokolnikov equation (CWKE), which is a well‐known equation in biology that shows how light‐attracted bacteria move together. This equation is very useful for analyzing pattern creation, instability regimes, and minor changes in linear situations since bacterial movement is very ...
Jan Muhammad +3 more
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Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation
Mathematics, 2020 This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of
Zakieh Avazzadeh +2 more
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On the Korteweg-de Vries equation
Manuscripta Mathematica, 1979 Existence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, with the initial function ϕ in the Sobolev space of order s>3/2 and the solution u(t) staying in the same space, s=∞ being included For the proper KdV equation, existence of ...
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Dispersive Hydrodynamics of Soliton Condensates for the Korteweg-de Vries Equation. [PDF]
J Nonlinear Sci, 2023 Congy T, El GA, Roberti G, Tovbis A.
europepmc +1 more source
On integrability of one third-order nonlinear evolution equation
, 2003 We study one third-order nonlinear evolution equation, recently introduced by Chou and Qu in a problem of plane curve motions, and find its transformation to the modified Korteweg - de Vries equation, its zero-curvature representation with an essential ...
Chou +8 more
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Learning the Nonlinear Solitary Wave Solution of the Korteweg-De Vries Equation with Novel Neural Network Algorithm. [PDF]
Entropy (Basel), 2023 Wen Y, Chaolu T.
europepmc +1 more source
Traveling wave solutions of a coupled Schrödinger-Korteweg-de Vries equation by the generalized coupled trial equation method. [PDF]
Heliyon, 2023 Shang J, Li W, Li D.
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Reductions of lattice mKdV to $q$-$\mathrm{P}_{VI}$
, 2011 This Letter presents a reduction of the lattice modified Korteweg-de-Vries equation that gives rise to a $q$-analogue of the sixth Painlev\'e equation.
Adler +13 more
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Negative-order Korteweg–de Vries equations
Physical Review E, 2012 In this paper, based on the regular Korteweg-de Vries (KdV) system, we study negative-order KdV (NKdV) equations, particularly their Hamiltonian structures, Lax pairs, conservation laws, and explicit multisoliton and multikink wave solutions thorough bilinear Bäcklund transformations.
Zhijun, Qiao, Engui, Fan
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Hamiltonian formulation for the description of interfacial solitary waves [PDF]
Nonlinear Processes in Geophysics, 1998 We consider solitary waves propagating on the interface between two fluids, each of constant density, for the case when the upper fluid is bounded above by a rigid horizontal plane, but the lower fluid has a variable depth.
R. Grimshaw, S. R. Pudjaprasetya
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