Results 91 to 100 of about 23,042 (190)
Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit
, 2009 We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior.
Claeys T. +7 more
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12427-12439, August 2025.ABSTRACT The Ostrovsky equation models long, weakly nonlinear waves, explaining the propagation of surface and internal waves in a rotating fluid. The study focuses on the generalized Ostrovsky equation. Introduced by Levandosky and Liu, this equation demonstrates the existence of solitary waves through variational methods.
Sol Sáez
wiley +1 more source
Physical vs mathematical origin of the extended KdV and mKdV equations
AIMS MathematicsThe higher-order Korteweg-de Vries (KdV) and modified KdV (mKdV) equations are derived from a physical model describing a three-component plasma composed of cold fluid ions and two species of Boltzmann electrons at different temperatures.
Saleh Baqer +2 more
doaj +1 more source
New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations
Applied Mathematics and Nonlinear Sciences, 2020 Abstract A large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. The procedure starts by reducing both equations to related ODEs by compatible travelling wave transforms.
Hadi Rezazadeh +4 more
openaire +1 more source
A well-posedness result for an extended KdV equation
Partial Differential Equations in Applied MathematicsAmong 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
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 +3 more
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Prohibitions caused by nonlocality for Alice-Bob Boussinesq-KdV type systems
, 2018 It is found that two different celebrate models, the Korteweg de-Vrise (KdV) equation and the Boussinesq equation, are linked to a same model equation but with different nonlocalities. The model equation is called the Alice-Bob KdV (ABKdV) equation which
Lou, S. Y.
core
Optimal system and dynamics of optical soliton solutions for the Schamel KdV equation. [PDF]
Sci Rep, 2023 Hussain A +4 more
europepmc +1 more source
On rational similarity solutions of $KdV$ and $m$-$KdV$ equations
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1983 This note presents rational similarity solutions \(u_ n\) in series for the KdV equation and \(v_ n\) for the modified-KdV equation. These solutions were expressed in terms of polynomials originally introduced by Yablonskij (1959) and Vorobiev (1965) to describe rational solutions of the second Painlevé equation.
openaire +3 more sources
A scalar Riemann-Hilbert problem on the torus: applications to the KdV equation. [PDF]
Anal Math Phys, 2022 Piorkowski M, Teschl G.
europepmc +1 more source