Asymptotic dynamics of short-waves in nonlinear dispersive models
, 1997 The multiple-scale perturbation theory, well known for long-waves, is extended to the study of the far-field behaviour of short-waves, commonly called ripples.
A. H. Nayfeh +14 more
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Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg-de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations. [PDF]
Entropy (Basel), 2022 Nikolova EV.
europepmc +1 more source
Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation
International Journal of Applied Mathematics and Computer Science, 2017 The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume ...
Yan Jin-Liang, Zheng Liang-Hong
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On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces [PDF]
, 2010 We study persistence properties of solutions to some canonical dispersive models, namely the semi-linear Schr\"odinger equation, the $k$-generalized Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev spaces $H^s(\R^n)\cap L^2 ...
Nahas, Joules, Ponce, Gustavo
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, 1997 We study solitary-wave and kink-wave solutions of a modified Boussinesq equation through a multiple-time reductive perturbation method. We use appropriated modified Korteweg-de Vries hierarchies to eliminate secular producing terms in each order of the ...
Manna, M. A., Merle, V.
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The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation [PDF]
, 2014 The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation $\boldsymbol{K} \boldsymbol{M}+\boldsymbol{M} \boldsymbol{K}=\boldsymbol{r}\, \boldsymbol{s}^{T}$
Xu, Dan-dan +2 more
core
The Korteweg-de Vries Equation
, 2013 Two page encyclopedic article about the Korteweg-de Vries equation covering historical perspective, solitary wave and periodic solutions, modern developments, properties and applications, and further reading.
openaire +2 more sources
A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations
Abstract and Applied Analysis, 2012 The present paper is devoted to the development of a new scheme to solve the initial-boundary value Korteweg-de Vries equation which models many physical phenomena such as surface water waves in a channel.
Ali H. Bhrawy, M. M. Al-Shomrani
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On the generalized Korteweg-de Vries-type equations
Differential and Integral Equations, 1997 The author investigates the Cauchy problem in \(\mathbb R^1\) for the generalized Korteweg-de Vries (KdV) equation with nonlinear term of the form \(F(u)\partial _x u\), and for an equation of mixed KdV and Schrödinger type. For the former equation the author proves the local well-posedeness assuming \(F(u)=u^2 g(u)\) with \(g(u)\) smooth, or global ...
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General rogue wave solutions and their dynamics in the complex modified Korteweg–de Vries equation
Results in PhysicsBy means of the Hirota bilinear method together with the Kadomtsev–Petviashvili hierarchy reduction technique, general higher-order rogue wave solutions of the complex modified Korteweg–de Vries equation are derived explicitly.
Yan Zhu +5 more
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