Results 61 to 70 of about 8,902 (211)
A Note on the Fractional Generalized Higher Order KdV Equation
Journal of Function Spaces, 2018 We obtain exact solutions to the fractional generalized higher order Korteweg-de Vries (KdV) equation using the complex method. It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations ...
Yongyi Gu
doaj +1 more source
Kinetic equation for a dense soliton gas [PDF]
, 2005 We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations.
A. M. Kamchatnov +7 more
core +3 more sources
An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation [PDF]
Proceedings of the National Academy of Sciences, 1998 This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way. We present, in particular, an algorithm, to obtain the support of the Riemann-Hilbert problem for leading asymptotics. Applying this extended method to small dispersion KdV (Korteweg-de Vries) equation, we (
Deift, P., Venakides, S., Zhou, X.
openaire +2 more sources
Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid +5 more
wiley +1 more source
The solution of fractional-order system of KdV equations with exponential-decay kernel
Results in Physics, 2022 This study uses efficient techniques to evaluate a non-linear system of Korteweg–de Vries (KdV) equations with fractional Caputo Fabrizio derivative, including the modified decomposition approach and the novel iterative transform method.
Mohammad Alshammari +3 more
doaj +1 more source
Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation [PDF]
, 2009 We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV equation in the ...
Ablowitz M +8 more
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Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended ...
Abdul Saboor +5 more
wiley +1 more source
Electronic Journal of Differential Equations, 2003 We present a new method for studying the interaction of solitons for non-integrable Korteweg-de Vries (KdV) type equations with small dispersion and test this method for the KdV equation.
Vladimir G. Danilov +1 more
doaj
On abundant new solutions of two fractional complex models
Advances in Difference Equations, 2020 We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg–de Vries equation (KdV) equation and the fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation).
Mostafa M. A. Khater, Dumitru Baleanu
doaj +1 more source
The Integrability of New Two-Component KdV Equation [PDF]
, 2010 We consider the bi-Hamiltonian representation of the two-component coupled KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich and Foursov. Connection of this equation with the supersymmetric Kadomtsev-Petviashvilli-Radul-Manin
Popowicz, Ziemowit
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