Results 61 to 70 of about 1,197 (185)

Modulational stability of Korteweg-de Vries and Boussinesq wavetrains

International Journal of Mathematics and Mathematical Sciences, 1983
The modulational stability of both the Korteweg-de Vries (KdV) and the Boussinesq wavetrains is investigated using Whitham's variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable.
Bhimsen K. Shivamoggi, Lokenath Debnath
doaj   +1 more source

A Regularization-Free Scheme for Recovering Large External Forces of Higher-Order Nonlinear Evolution Equations

Axioms, 2023
In this study, the inverse engineering problems of the Ostrovsky equation (OE), Kawahara equation (KE), modified Kawahara equation (mKE), and sixth-order Korteweg-de Vries (KdV) equation will be investigated numerically.
Chih-Wen Chang
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

Computing the Solutions of the Combined Korteweg-de Vries Equation by Turing Machines [PDF]

Electronic Proceedings in Theoretical Computer Science, 2010
In this paper, we study the computability of the initial value problem of the Combined KdV equation. It is shown that, for any integer s>2, the nonlinear solution operator which maps an initial condition data to the solution of the Combined KdV ...
Dianchen Lu, Qingyan Wang, Rui Zheng
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

Development and Cancellation of Long‐Duration Positive Ionospheric Storms: Both Changes of the F2‐Layer Peak Height and O/N2 Ratio Can Be Decisive

Space Weather, Volume 24, Issue 7, July 2026.
Abstract For decades, two competing hypotheses on the key drivers of mid‐latitude long‐duration positive ionospheric storms (LDPS) have been considered: (a) an increase of the F2‐layer peak height (hmF2) and (b) an increase in the atomic oxygen to molecular nitrogen density ratio (O/N2).
D. V. Kotov, M. O. Reznychenko, P. G. Richards, O. V. Bogomaz, L. P. Goncharenko, L. J. Paxton, M. Hernández‐Pajares, A. I. Reznychenko, D. P. Shkonda, V. V. Barabash, L. Ya. Emelyanov, I. F. Domnin, A. Ye. Miroshnikov, V. P. Burmaka, D. A. Dzyubanov, Yu. I. Podyachiy   +15 more
wiley   +1 more source

Numerical simulation of a solitonic gas in KdV and KdV–BBM equations [PDF]

Physics Letters A, 2014
19 pages, 11 figures, 47 references. Other author's papers can be found at http://www.denys-dutykh.com/
Denys Dutykh, Efim Pelinovsky
openaire   +3 more sources

Exact Solutions and Nonlinear Dynamical Behavior in a Navier‐Stokes‐Type Model for Elastic Cylindrical Vessels: An Analytical and Computational Approach

Engineering Reports, Volume 8, Issue 6, June 2026.
This study investigates a nonlinear Navier‐Stokes‐type model for elastic cylindrical vessels. Exact solutions are derived via the Bäcklund transformation and the ϕ6$$ {\phi}^6 $$‐expansion method, and dynamical behaviors are analyzed using bifurcation and chaos tools, revealing diverse wave structures and parameter‐dependent propagation characteristics.
Sheikh Zain Majid, Fatma Nur Kaya Sağlam, Mohammad Safi Ullah   +2 more
wiley   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source