Results 71 to 80 of about 18,115 (195)

The Generalized Harry Dym Equation

, 2003
The Harry Dym equation is generalized to the system of equations in the manner as the Korteweg - de Vries equation is generalized to the Hirota - Satsuma equation . The Lax and Hamiltonian formulation for this generalization is given.This generalized Lax
Adler, Alber, Antonowicz, Brunelli, Brunelli, Błaszak, Dodd, Gelfand, Hirota, Konopelchenko, Manna, Ziemowit Popowicz   +11 more
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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, Olver, S.Yu. Sakovich, Sakovich, Sakovich, Sakovich, Sakovich, Wadati, Wadati   +8 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, Omid Nikan, José A. Tenreiro Machado   +2 more
doaj   +1 more source

Korteweg-de Vries Equation in Bounded Domains

Boletim da Sociedade Paranaense de Matemática, 2009
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On the origin of the Korteweg-de Vries equation

, 2011
The Korteweg-de Vries equation has a central place in a model for waves on shallow water and it is an example of the propagation of weakly dispersive and weakly nonlinear waves.
de Jager, E. M.
core  

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
core   +2 more sources

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, Christopher M. Ormerod, Grammaticos, Hay, Jimbo, Joshi, Joshi, Kakei, Ormerod, Papageorgiou, Papageorgiou, Quispel, Ramani, Tokihiro   +13 more
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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 the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations

, 2008
We solve the Cauchy problem for the Korteweg-de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption that the respective spectral bands either coincide or are disjoint.Comment:
Baranetskii V B, Belokolos E D, Bikbaev R F, Bikbaev R F, Bondareva I, Bondareva I N, Boutet de Monvel A, Buslaev V S, Eckhaus W, Egorova I Teschl G, Ermakova V D, Ermakova V D, Faddeev L D, Firsova N E, Firsova N E, Gerald Teschl, Gesztesy F, Gesztesy F Ratnaseelan R Teschl G Gohberg I, Iryna Egorova, Its A R, Kamvissis S Teschl G, Kamvissis S Teschl G, Katrin Grunert, Khruslov E Ya, Khruslov E Ya, Khruslov E Ya, Khruslov E Ya, Khruslov E Ya, Krüger H Teschl G, Kuznetsov E A, Lax P D, Levitan B M, Marchenko V A, Novikov S P   +33 more
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Darboux transformations for supersymmetric korteweg-de vries equations [PDF]

Letters in Mathematical Physics, 1995
\hspace{.2in}We consider the Darboux type transformations for the spectral problems of supersymmetric KdV systems. The supersymmetric analogies of Darboux and Darboux-Levi transformations are established for the spectral problems of Manin-Radul-Mathieu sKdV and Manin-Radul sKdV. Several B cklund transformations are derived for the MRM sKdV and MR sKdV
openaire   +3 more sources