Results 81 to 90 of about 22,064 (260)

Weak asymptotic method for the study of propagation and interaction of infinitely narrow delta-solitons

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, Georgii A. Omel'yanov   +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

Emergence of Coupled Korteweg–de‐Vries Equations in m$m$ Fields

Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.
ABSTRACT The Korteweg–de‐Vries (KdV) equation is of fundamental importance in a wide range of subjects with generalization to multi‐component systems relevant for multi‐species fluids and cold atomic mixtures. We present a general framework in which a family of multi‐component KdV (mcKdV) equations naturally arises from a broader mathematical structure
Sharath Jose, Manas Kulkarni, Vishal Vasan   +2 more
wiley   +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, Agrawal G P, Grimshaw R, Grimshaw R, Holloway P, Karpman V I, Ma W X, Newell A C, Yeojin Chung   +8 more
core   +1 more source

Global well-posedness for dissipative Korteweg-de Vries equations [PDF]

, 2007
This paper is devoted to the well-posedness for dissipative KdV equations ut + uxxx + |Dx|2αu + uux = 0, 0 -3/4 for α ≤ 1/2 and s > -3/(5-2α) for α > 1/2.
Stéphane Vento
semanticscholar   +1 more source

Finite‐Dimensional Reductions and Finite‐Gap‐Type Solutions of Multicomponent Integrable PDEs

Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.
ABSTRACT The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well‐known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup ...
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev   +2 more
wiley   +1 more source

White-Noise-Driven KdV-Type Boussinesq System

Mathematics
The white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize features from both the ...
Aissa Boukarou, Safa M. Mirgani, Khaled Zennir, Keltoum Bouhali, Sultan S. Alodhaibi   +4 more
doaj   +1 more source

Andrew Lenard: A Mystery Unraveled [PDF]

, 2005
The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the "Lenard recursion formula". The story about the discovery of the formula told by Andrew Lenard is the subject of this article.Comment: Published in SIGMA (Symmetry,
Praught, Jeffery, Smirnov, Roman G.
core   +2 more sources

Quasimodular instanton partition function and the elliptic solution of Korteweg–de Vries equations [PDF]

, 2014
The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint
Wei He
semanticscholar   +1 more source

Nonlinear inference capacity of fiber‐optical extreme learning machines

Nanophotonics, Volume 14, Issue 16, Page 2749-2760, August 2025.
Abstract The intrinsic complexity of nonlinear optical phenomena offers a fundamentally new resource to analog brain‐inspired computing, with the potential to address the pressing energy requirements of artificial intelligence. We introduce and investigate the concept of nonlinear inference capacity in optical neuromorphic computing in highly nonlinear
Sobhi Saeed, Mehmet Müftüoğlu, Glitta R. Cheeran, Thomas Bocklitz, Bennet Fischer, Mario Chemnitz   +5 more
wiley   +1 more source