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
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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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.
europepmc +1 more source
Asymptotic dynamics of short-waves in nonlinear dispersive models
, 1997 The multiple-scale perturbation theory, well known for long-waves, is extended to the study of the far-field behaviour of short-waves, commonly called ripples.
A. H. Nayfeh +14 more
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, 1997 We study solitary-wave and kink-wave solutions of a modified Boussinesq equation through a multiple-time reductive perturbation method. We use appropriated modified Korteweg-de Vries hierarchies to eliminate secular producing terms in each order of the ...
Manna, M. A., Merle, V.
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Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg-de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations. [PDF]
Entropy (Basel), 2022 Nikolova EV.
europepmc +1 more source
On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces [PDF]
, 2010 We study persistence properties of solutions to some canonical dispersive models, namely the semi-linear Schr\"odinger equation, the $k$-generalized Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev spaces $H^s(\R^n)\cap L^2 ...
Nahas, Joules, Ponce, Gustavo
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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
doaj