Results 171 to 180 of about 18,045 (194)
Some of the next articles are maybe not open access.
New exact solutions for Korteweg-de Vries Burgers equation and Korteweg-de Vries equation
MSIE 2011, 2011To obtain new exact solutions for Korteweg-de Vries Burgers equation and Korteweg-de Vries equation, with the aid of symbolic computation, the Korteweg-de Vries Burgers equation and Korteweg-de Vries equation are investigated by using the trigonometric function transform method.
DongBo Cao, null LiuXian Pan, JiaRen Yan
openaire +1 more source
2007
In this chapter we consider weakly nonlinear long waves. Here the basic paradigm is the well-known Korteweg-de Vries equation and its solitary wave solution. We present a brief historical discussion, followed by a typical derivation in the context of internal and surface water waves.
openaire +1 more source
In this chapter we consider weakly nonlinear long waves. Here the basic paradigm is the well-known Korteweg-de Vries equation and its solitary wave solution. We present a brief historical discussion, followed by a typical derivation in the context of internal and surface water waves.
openaire +1 more source
The Korteweg-de Vries Equation
1998The Korteweg-de Vries equation, $$ {u_t} + u{u_x} + {u_{xxx}} = 0 $$ (3.1.1) is the simplest equation that includes both the effects of nonlinearity and dispersion. The equation appears in various forms in the literature, sometimes with a factor of 6 or -6 in front of the nonlinear term.
Carlo Cercignani, David H. Sattinger
openaire +1 more source
Hierarchies of Korteweg–de Vries type equations
Journal of Mathematical Physics, 1995An eigenvalue problem is considered. New hierarchies of bi-Hamiltonian systems are constructed. Some examples of these systems and their reductions are presented.
openaire +1 more source
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. M. Khader, Khaled M. Saad
openaire +1 more source
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. M. Khader, Khaled M. Saad
openaire +1 more source
Water waves and Korteweg–de Vries equations
Journal of Fluid Mechanics, 1980The classical problem of water waves on an incompressible irrotational flow is considered. By introducing an appropriate non-dimensionalization, we derive four Korteweg–de Vries equations: two expressed in Cartesian co-ordinates and two in plane polars.
openaire +2 more sources
Coupled Korteweg–de Vries Equations
2013When a system supports two distinct long-wave modes with nearly coincident phase speeds, the weakly nonlinear and linear dispersion unfolding generically leads to two coupled Korteweg–de Vries equations. In this paper, we review the derivation of such systems in stratified fluids, extending previous studies by allowing for background shear flows ...
openaire +1 more source
The Korteweg-de Vries equation and beyond
Acta Applicandae Mathematicae, 1995The author reviews a new method for linearizing the initial-boundary value problem of the Korteweg-de Vries (KdV) equation on the semi-infinite line for decaying initial and boundary data. The author also presents a novel class of physically important integrable equations.
openaire +2 more sources
The Korteweg-de Vries-Burgers equation
Journal of Computational Physics, 1977Abstract The time evolution and stability of the shock solutions of the Korteweg-de Vries-Burgers equation are studied numerically. It is found that nonanalytic initial data satisfying the boundary conditions of the problem evolve asymptotically into the steady-state shocks predicted by a time-independent analysis.
Canosa, Jose, Gazdag, Jenö
openaire +2 more sources
Journal of Mathematical Physics, 1971
It is shown that if a function of x and t satisfies the Korteweg-de Vries equation and is periodic in x, then its Fourier components satisfy a Hamiltonian system of ordinary differential equations. The associated Poisson bracket is a bilinear antisymmetric operator on functionals.
openaire +1 more source
It is shown that if a function of x and t satisfies the Korteweg-de Vries equation and is periodic in x, then its Fourier components satisfy a Hamiltonian system of ordinary differential equations. The associated Poisson bracket is a bilinear antisymmetric operator on functionals.
openaire +1 more source