Results 61 to 70 of about 1,252 (111)
Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves
Results in Physics, 2019 In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived ...
Essam. R. El-Zahar, Hilmi Demiray
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Prolongation structure of the Krichever-Novikov equation [PDF]
, 2002 We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, u_x, u_{xx}, u_{xxx} for the Krichever-Novikov equation u_t=u_{xxx}-3u_{xx}^2/(2u_x)+p(u)/u_x+au_x in the case when the polynomial p(u)=4u^3-g_2u-g_3 has ...
Igonin, Sergei, Martini, Ruud
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Decay Rate on the Radius of Spatial Analyticity to Solutions for the Modified Camassa–Holm Equation
Journal of Mathematics, Volume 2025, Issue 1, 2025.The initial value problem associated with the modified Camassa–Holm equation for initial data u0(x) that is analytic on the line and having uniform radius of spatial analyticity σ0 is considered. We have shown the persistence of the radius of spatial analyticity till some time δ.
Tegegne Getachew, Yongqiang Fu
wiley +1 more source
Soliton equations: admitted solutions and invariances via B\"acklund transformations [PDF]
Open Communications in Nonlinear Mathematical PhysicsA couple of applications of B\"acklund transformations in the study of nonlinear evolution equations is here given. Specifically, we are concerned about third order nonlinear evolution equations.
Sandra Carillo, Cornelia Schiebold
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Soliton surfaces associated with symmetries of ODEs written in Lax representation
, 2011 The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs ...
A M Grundland +11 more
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The initial-value problem for a Gardner-type equation
Advanced Nonlinear StudiesDiscussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry +4 more
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Communications in Computational Physics, 2019 We consider a midpoint scheme to approximate analytical solutions to a white noise driven BBM equation that reads du−duxx+ux◦dW+uuxdt=0. We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is
Guillaume Fenger
semanticscholar +1 more source
Wave breaking of periodic solutions to the Fornberg-Whitham equation
, 2017 Based on recent well-posedness results in Sobolev (or Besov spaces) for periodic solutions to the Fornberg-Whitham equations we investigate here the questions of wave breaking and blow-up for these solutions.
Hoermann, Guenther
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Peaked solitary waves and shock waves of the Degasperis-Procesi-Kadomtsev-Petviashvili equation
Advances in Nonlinear AnalysisIn this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect.
Moon Byungsoo, Yang Chao
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Multipeakons and a theorem of Stieltjes
, 1999 A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions.
Beals R +6 more
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