Results 61 to 70 of about 1,225,202 (162)

A Hybrid ML‐PDE Framework for Predicting Breaking Ocean Waves

Journal of Geophysical Research: Machine Learning and Computation, Volume 3, Issue 4, August 2026.
Abstract Wave breaking plays a central role in ocean dynamics, dissipating wave energy and shaping the evolution of the sea surface. Yet, breaking remains difficult to model: envelope‐based models efficiently capture nonlinear wave evolution and are interpretable but exclude breaking, while high‐fidelity direct numerical simulations resolve breaking ...
Y. Liu, T. A. A. Adcock, T. S. van den Bremer, D. Eeltink   +3 more
wiley   +1 more source

Solitary Waves of Moderate Amplitude and Dispersive Radiation in the Serre Equations: The Extended KdV–Whitham Approximation

Studies in Applied Mathematics, Volume 157, Issue 2, August 2026.
ABSTRACT We consider the extended Korteweg–de Vries (eKdV) equation as a model for long moderately nonlinear surface water waves and use it to describe the evolution of initial conditions generating solitary waves with and without significant dispersive radiation, as well as cases of pure dispersive radiation without any solitary waves.
Benjamin Martin, Dmitri Tseluiko, Karima Khusnutdinova   +2 more
wiley   +1 more source

Insensitizing control of KDV–Burgers equations

Journal of Electrical Systems and Information Technology, 2018
This paper deals with the problem of insensitizing control of KDV–Burgers equation. This analysis produces a special type of null controllability, and shows that the nonlinear KDV–Burgers equation can be solved in terms of an insensitizing control.
Ravi Kumar Rajagounder, Chong Kil To
doaj   +1 more source

KdV limit for the Vlasov–Poisson–Landau system

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We are concerned with the fluid limit to KdV equations for the one‐dimensional Vlasov–Poisson–Landau system that describes the dynamics of ions in plasma with the electron density determined by the self‐consistent electric potential through the so‐called Boltzmann relation. Formally, it is well known that as the Knudsen number ε→0$\varepsilon \
Renjun Duan, Dongcheng Yang, Hongjun Yu
wiley   +1 more source

On the discrete and continuous Miura chain associated with the sixth Painlev equation [PDF]

, 2000
A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or B\"acklund transformations. We describe such a chain for the sixth Painlev\'e equation (\pvi), containing, apart from \pvi itself, a Schwarzian ...
Hone, A. N. W., Nijhoff, F., Nijhoff, Frank W., Joshi, Nalini, Frank Nijhoff, Joshi, N., Nalini Joshi, Andrew Hone, Hone, Andrew N.W.   +8 more
core   +1 more source

Traveling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena

AIP Advances, 2014
In this paper, KdV-Burger-Kuramoto equation involving instability, dissipation, and dispersion parameters is solved numerically. The numerical solution for the fractional order KdV-Burger-Kuramoto (KBK) equation has been presented using two-dimensional ...
A. K. Gupta, S. Saha Ray
doaj   +1 more source

Uncertainty Quantification of Analytical Solutions for the Nonlinear Space and Time Fractional Order ϕ4$$ {\phi}^4 $$ Equation Under Fuzziness

Engineering Reports, Volume 8, Issue 7, July 2026.
Analytical fuzzy soliton solutions of a modified space–time fractional ϕ4$$ {\phi}^4 $$ model are derived using EHFM, capturing memory effects and uncertainty. Results reveal diverse wave structures and show how fractional order and fuzziness significantly influence soliton amplitude, localization, and propagation, with heightened sensitivity near the ...
Mohsin Khalid, Neha Andaleeb Khalid, Baboucarr Ceesay, Zafar Iqbal   +3 more
wiley   +1 more source

A well-posedness result for an extended KdV equation

Partial Differential Equations in Applied Mathematics
Among the most interesting things Russell discovered was there is a mathematical relation between the height of the wave, the depth of the wave when water at rest and the speed at which the wave travels.
M. Berjawi, T. El Arwadi, S. Israwi
doaj   +1 more source

Stability of a Fully Discrete Local Discontinuous Galerkin Method for the Generalized Benjamin–Ono Equation

Numerical Methods for Partial Differential Equations, Volume 42, Issue 4, July 2026.
ABSTRACT The main purpose of this paper is to design a fully discrete local discontinuous Galerkin (LDG) scheme for the generalized Benjamin–Ono equation. First, we prove the L2$$ {L}^2 $$‐stability for the proposed semi‐discrete LDG scheme and obtained a suboptimal order of convergence for power nonlinear flux.
Mukul Dwivedi, Tanmay Sarkar
wiley   +1 more source

A Convergent Fourier Spectral Galerkin Method for the Fractional Camassa–Holm Equation

Numerical Methods for Partial Differential Equations, Volume 42, Issue 4, July 2026.
ABSTRACT We analyze a Fourier spectral Galerkin method for the fractional Camassa–Holm (fCH) equation involving a fractional Laplacian of exponent α∈[1,2]$$ \alpha \in \left[1,2\right] $$ with periodic boundary conditions. The semi‐discrete scheme preserves both mass and energy invariants of the fCH equation.
Mukul Dwivedi, Andreas Rupp
wiley   +1 more source