Results 1 to 10 of about 22,064 (260)

Two Kinds of New Integrable Couplings of the Negative-Order Korteweg-de Vries Equation

Advances in Mathematical Physics, 2015
Based on some known loop algebras with finite dimensions, two different negative-order integrable couplings of the negative-order Korteweg-de Vries (KdV) hierarchy of evolution equations are generated by making use of the Tu scheme, from which the ...
Binlu Feng, Yufeng Zhang
doaj   +1 more source

Conservation laws and normal forms of evolution equations

, 2010
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws.
Abellanas, Abellanas, Abellanas, Abellanas, Artur Sergyeyev, Ashton, Bocharov, Bryant, Błaszak, Drinfel'd, Foltinek, Foltinek, Galindo, Ibragimov, Igonin, Kaptsov, Kunzinger, Magadeev, Mikhailov, Mikhailov, Mikhailov, Miura, Newell, Nikitin, Olver, Popovych, Popovych, Popovych, Popovych, Roman O. Popovych, Sanders, Sanders, Sanders, Sergyeyev, Shapovalov, Svinolupov   +35 more
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Higher order terms in multiscale expansions: a linearized KdV hierarchy [PDF]

, 2001
We consider a wide class of model equations, able to describe wave propagation in dispersive nonlinear media. The Korteweg-de Vries (KdV) equation is derived in this general frame under some conditions, the physical meanings of which are clarified. It is
Leblond, H.
core   +4 more sources

An efficient approach for the numerical solution of fifth-order KdV equations

Open Mathematics, 2020
The main aim of this article is to use a new and simple algorithm namely the modified variational iteration algorithm-II (MVIA-II) to obtain numerical solutions of different types of fifth-order Korteweg-de Vries (KdV) equations.
Ahmad Hijaz, Khan Tufail A., Yao Shao-Wen   +2 more
doaj   +1 more source

Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations

, 2002
In a recent paper, Kenig, Ponce and Vega study the low regularity behavior of the focusing nonlinear Schr\"odinger (NLS), focusing modified Korteweg-de Vries (mKdV), and complex Korteweg-de Vries (KdV) equations.
Christ, Michael, Colliander, James, Tao, Terence   +2 more
core   +4 more sources

Numerical Wave Solutions for Nonlinear Coupled Equations using Sinc-Collocation Method

Sultan Qaboos University Journal for Science, 2015
In this paper, numerical solutions for nonlinear coupled Korteweg-de Vries(abbreviated as KdV) equations are calculated by the Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. The first step is to
Kamel Al-Khaled
doaj   +1 more source

On a Schwarzian PDE associated with the KdV Hierarchy [PDF]

, 1999
We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy.
Ablowitz, Ablowitz, Andrew Hone, Fokas, Frank Nijhoff, Fuchs, Fuchs, Gromak, Konopelchenko, Martina, Miwa, Nalini Joshi, Nijhoff, Okamoto, Okamoto, P Burtsev, Tod, Weiss, Weiss   +18 more
core   +2 more sources

Integrability of reductions of the discrete Korteweg–de Vries and potential Korteweg–de Vries equations [PDF]

Proceedings of the Royal Society A, 2012
We study the integrability of mappings obtained as reductions of the discrete Korteweg–de Vries (KdV) equation and of two copies of the discrete potential KdV (pKdV) equation.
A. Hone, Peter H. van der Kamp, G. Quispel, D. T. Tran   +3 more
semanticscholar   +1 more source

KdV and mKdV Ion-Acoustic Solitary Waves In a Positron-beam Plasma with Kaniadakis Distributed Electrons

East European Journal of Physics
Theoretical and numerical studies of ion-acoustic solitary waves (IASWs) in an unmagnetized plasma with ions, positron beams under pressure variation, and kaniadakis distributed electrons have been conducted. The potential wave amplitude is calculated by
Rafia Khanam, Satyendra Nath Barman
doaj   +1 more source

Classification of Multiply Travelling Wave Solutions for Coupled Burgers, Combined KdV-Modified KdV, and Schrödinger-KdV Equations

Abstract and Applied Analysis, 2015
Some explicit travelling wave solutions to constructing exact solutions of nonlinear partial differential equations of mathematical physics are presented.
A. R. Seadawy, K. El-Rashidy
doaj   +1 more source