Results 81 to 90 of about 17,995 (145)

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

Chiral Solitons in Generalized Korteweg-de Vries Equations

, 1998
Generalizations of the Korteweg-de Vries equation are considered, and some explicit solutions are presented. There are situations where solutions engender the interesting property of being chiral, that is, of having velocity determined in terms of the ...
Aglietti, Bazeia, Bazeia, Bazeia, Beneton Rabello, Beneton Rabello, Coffey, D. Bazeia, Das, Debnath, Dey, F. Moraes, Griguolo, Hereman, Iwao, Jackiw, Korteweg, Rajaraman, Rajaraman, Ruck, Whitham   +20 more
core   +2 more sources

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

Exploration traveling solitary solutions to the modified Korteweg-de Vries equation with advection noise

AIMS Mathematics
In this study, we investigate the stochastic modified Korteweg-de Vries (SmKdV) equation, which is driven in the Itô sense by advection noise. We show that by solving certain deterministic counterparts of the modified Korteweg-de Vries with an extra ...
Sofian T. Obeidat, Doaa Rizk, Wael W. Mohammed   +2 more
doaj   +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  

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

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