Results 71 to 80 of about 1,197 (185)

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

Stability of KdV Solitons on the Half‐Line: A Study for Nonhomogeneous Boundary Conditions

Studies in Applied Mathematics, Volume 156, Issue 6, June 2026.
ABSTRACT We study the orbital stability and asymptotic stability problems for KdV solitons on the right half‐line for nonhomogeneous boundary conditions in the energy space H1(R+)$H^1(\mathbb {R}^+)$. This paper improves the results of Cavalcante and Muñoz [Revista Matemática Iberoamericana 35, no. 6 (2019); and SIAM Journal on Mathematical Analysis 55,
Luccas Campos, Mykael Cardoso, Márcio Cavalcante   +2 more
wiley   +1 more source

The Interactions of N-Soliton Solutions for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Advances in Mathematical Physics, 2015
A generalized (2+1)-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the (1+1)-dimensional KdV equation.
Xiangrong Wang, Xiaoen Zhang, Yong Zhang, Huanhe Dong   +3 more
doaj   +1 more source

Existence of Solitary Waves in a Perturbed KdV-mKdV Equation

Journal of Mathematics, 2021
In this paper, we establish the existence of a solitary wave in a KdV-mKdV equation with dissipative perturbation by applying the geometric singular perturbation technique and Melnikov function.
Chengqun Li, Minzhi Wei, Yuanhua Lin
doaj   +1 more source

Internal Wave Characteristics in the Andaman Sea: New Insights From SWOT Observations

Geophysical Research Letters, Volume 53, Issue 10, 28 May 2026.
Abstract High‐resolution, repeat‐pass Sea Surface Height Anomaly (SSHA) observations from the Surface Water and Ocean Topography (SWOT) satellite are used to investigate Internal Solitary Waves (ISW) in the Andaman Sea over a one‐year period starting in July 2023. SWOT captured surface signatures of high‐amplitude ISW, with SSHA exceeding 20 cm.
Anup Kumar Mandal, Aditya Chaudhary, Seemanth M, Ratheesh Ramakrishnan, Neeraj Agarwal, Rashmi Sharma, R. Venkat Shesu, T. V. S Udaya Bhaskar   +7 more
wiley   +1 more source

Rational approximate symmetries of KdV equation [PDF]

Journal of Physics A: Mathematical and General, 2003
We construct one-parameter deformation of the Dorfman Hamiltonian operator for the Riemann hierarchy using the quasi-Miura transformation from topological field theory. In this way, one can get the approximately rational symmetries of KdV equation and then investigate its bi-Hamiltonian structure.
openaire   +3 more sources

Quasi-integrability of deformations of the KdV equation [PDF]

Nuclear Physics B, 2019
We investigate the quasi-integrability properties of various deformations of the Korteweg-de Vries (KdV) equation, depending on two parameters $\varepsilon_1$ and $\varepsilon_2$, which include among them the regularized long-wave (RLW) and modified regularized long-wave (mRLW) equations.
F. ter Braak, L.A. Ferreira, W.J. Zakrzewski   +2 more
openaire   +5 more sources

Free Surface Waves in Electrohydrodynamics With a Prescribed Vorticity Distribution

Mathematical Methods in the Applied Sciences, Volume 49, Issue 7, Page 7068-7081, 15 May 2026.
ABSTRACT Traditionally, the study of free surface flows assumed irrotationality to simplify matters, and the results seemed to have great success, notably with the Korteweg‐de Vries(KdV) equation. In the past decade, there have been attempts to remove this seemingly strong condition and replace it with a global constant vorticity equivalent to a linear
M. J. Hunt, Denys Dutykh
wiley   +1 more source

An exponential-type integrator for the KdV equation

Numerische Mathematik, 2016
We introduce an exponential-type time-integrator for the KdV equation and prove its first-order convergence in $H^1$ for initial data in $H^3$. Furthermore, we outline the generalization of the presented technique to a second-order method.
Hofmanová, M., Schratz, K.
openaire   +5 more sources

An Explicit Construction of Kaleidocycles by Elliptic Theta Functions

Studies in Applied Mathematics, Volume 156, Issue 5, May 2026.
ABSTRACT We study a configuration space consisting of ordered points on the two‐dimensional sphere satisfying a system of quadratic constraints. We construct explicit periodic orbits in the configuration space using elliptic theta functions. The constructed orbits simultaneously satisfy semi‐discrete analogues of the modified KdV and sine‐Gordon ...
Shizuo Kaji, Kenji Kajiwara, Shota Shigetomi   +2 more
wiley   +1 more source