Results 91 to 100 of about 59,617,543 (217)

Using Crank-Nikolson Scheme to Solve the Korteweg-de Vries (KdV) Equation

CoRR
The Korteweg-de Vries (KdV) equation is a fundamental partial differential equation that models wave propagation in shallow water and other dispersive media. Accurately solving the KdV equation is essential for understanding wave dynamics in physics and engineering applications.
openaire   +3 more sources

Nonlocal KdV equations

, 2020
Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korteweg-de Vries (KdV), complex KdV, and new nonlocal KdV equations. We obtain
Pekcan, ASLI, Gürses, Metin, Pekcan, A.
core   +1 more source

Painlevé integrability and multiple soliton solutions for the extensions of the (modified) Korteweg-de Vries-type equations with second-order time-derivative

Alexandria Engineering Journal
This work introduces two (3+1)-dimensional expansions of the Korteweg–de Vries (KdV) and modified KdV (mKdV) equations. These extensions incorporate a second-order time-derivative term, similar to the Boussinesq equation. The Painlevé test is utilized to
Abdul-Majid Wazwaz, Weaam Alhejaili, R.T. Matoog, S.A. El-Tantawy   +3 more
doaj   +1 more source

Lax representation with first-order operators for new nonlinear Korteweg – de Vries type equations

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022
Background. In this work, a new representation is constructed for equations of the Korteweg – de Vries (KdV) type. The proposed approach allows to obtain a universal Lax representation for a set of nonlinear partial differential equations, for which ...
V.M. Zhuravlev, V.M. Morozov
doaj   +1 more source

Helical solitons in vector modified Korteweg-de Vries equations

, 2018
We study existence of helical solitons in the vector modified Korteweg-de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable.
Stepanyants, Yury A., Pelinovsky, Dmitry E.   +1 more
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Negative-order Korteweg–de Vries equations [PDF]

, 2012
In this paper, based on the regular Korteweg–de Vries (KdV) system, we study negative-order KdV (NKdV) equations, particularly their Hamiltonian structures, Lax pairs, conservation laws, and explicit multisoliton and multikink wave solutions thorough ...
Fan, Engui, Qiao, Zhijun
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Shallow water cnoidal wave interactions [PDF]

Nonlinear Processes in Geophysics, 1994
The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV) and Kadomtsev-Petvishvilli (KP) equations, are considered.
A. R. Osborne
doaj  

Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation

Advances in Mathematical Physics, 2017
The Korteweg-de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice.
Dianchen Lu, Chen Yue, Muhammad Arshad
doaj   +1 more source

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He’s Polynomial

Nonlinear Engineering, 2017
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM).
Sharma Dinkar, Singh Prince, Chauhan Shubha   +2 more
doaj   +1 more source

Continuación única de soluciones de la ecuación de Korteweg-de Vries (KdV) [PDF]

, 2011
En el presente trabajo demostramos un principio de continuación única de soluciones para la ecuación de Korteweg-de Vries (KdV) ∂u/∂t + (∂^3)u/∂x^3 + u(∂u/∂x)=0; u=u(x,t), x ∈ R, t≥0, que afirma lo siguiente: Si u1, u2 ∈ C([0,1]; H^6(R)∩L^2((1 + x^2)^2α ...
Gutiérrez Jiménez, Nelson Jades
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