Results 61 to 70 of about 18,070 (146)

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
core   +1 more source

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
core   +2 more sources

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

Bi-differential calculus and the KdV equation

, 1999
A gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A is an N-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential) equations, are ...
A Dimakis, Brezin, Curtright, Dimakis, Dimakis, Dimakis, Dimakis, F Müller-Hoissen, Kruskal, Miura   +9 more
core   +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.
europepmc   +1 more source

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  

Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation

International Journal of Applied Mathematics and Computer Science, 2017
The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume ...
Yan Jin-Liang, Zheng Liang-Hong
doaj   +1 more source