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Linear superposition of Wronskian rational solutions to the kdv equation

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Communications in Theoretical Physics 2021年第6期73卷 1-5页

作者： Wen-Xiu Ma Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700United States of America School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

A linear superposition is studied for Wronskian rational solutions to the Kd V equation,which include rogue wave *** is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V *** is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.

关键词： soliton equation Wronskian solution rational solution rogue wave the kdv equation

Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the kdv equation without Loss of Regularity

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Annals of Applied Mathematics 2021年第1期37卷 1-21页

作者： Yongsheng Li Yifei Wu Fangyan Yao School of Mathematical Sciences South China University of TechnologyGuangzhouGuangdong 510640China Center for Applied Mathematics Tianjin UniversityTianjin 300072China

In this paper,we study the convergence rate of an Embedded exponential-type low-regularity integrator(ELRI)for the Korteweg-de Vries *** develop some new harmonic analysis techniques to handle the"stability"*** particular,we use a new stability estimate which allows us to avoid the use of the fractional Leibniz inequality,||■||f||H^(γ)^(2)||g||H^(γ+1),and replace f *** on these techniques,we prove that the ELRI scheme proposed in[41]provides 1/2-order convergence accuracy in H^(γ)for any initial data belonging to H^(γ)with γ>3/2,which does not require any additional derivative assumptions.

关键词： the kdv equation numerical solution convergence analysis error estimate low regularity fast Fourier transform

A kdv-Type Wronskian Formulation to Generalized KP, BKP and Jimbo–Miwa equations

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Communications in Theoretical Physics 2017年第7期67卷 1-5页

作者： Li Cheng Yi Zhang Normal School Jinhua Polytechnic Jinhua 321007 China Department of Mathematics Zhejiang Normal University Jinhua 321004 China

The purpose of this paper is to introduce a class of generaJized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A kdv-type Wronskian formulation is constructed by employing the Wronskian conditions of the kdv equation. Applications are made for the （3＋1）- dimensional generalized KP, BKP and Jimbo-Miwa equations, thereby presenting their Wronskian sufficient conditions. An N-soliton solution in terms of Wronskian determinant is obtained. Under a dimensional reduction, our results yield Wronskian solutions of the kdv equation.

关键词： generalized KP BKP and Jimbo-Miwa equations the kdv equation Wronskian formulation dimensional reduction

FORCED OSCILLATIONS OF A CLASS OF NONLINEAR DISPERSIVE WAVE equationS AND THEIR STABILITY

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Journal of Systems Science & Complexity 2007年第2期20卷 284-292页

作者： Muhammad USMAN Bingyu ZHANG Department of Mathematical Sciences University of Cincinnati Cincinnati Ohio 45221-0025 USA

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Korteweg-de Vries （kdv） equation and the damped Benjamin-Bona-Mahony （BBM） equation. In this paper we intend to show the same results hold for the pure kdv equation （without the damping terms） posed on a finite domain. Consideration is given to the initial-boundary-value problem {ut＋ux＋uux＋uxxx=0, u（x,0）=φ（x）, 0〈x〈1, t〉0,u（0,t）=h（t）, u（1,t） = 0, ux（1,t） = 0, t〉*** is shown that if the boundary forcing h is periodic with small ampitude, then the small amplitude solution u of （＊） becomes eventually time-periodic. Viewing （＊）（without the initial condition） as an infinite-dimensional dynamical system in the Hilbert space L^2（0, 1）, we also demonstrate that for a given periodic boundary forcing with small amplitude, the system （＊） admits a （locally） unique limit cycle, or forced oscillation, which is locally exponentially stable. A list of open problems are included for the interested readers to conduct further investigations.

关键词： Forced oscillation stability the BBM equation the kdv equation time-periodic solution

Derivative Instability of Some Schemes for the Korteweg-de Vries equation

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Communications in Nonlinear Science and Numerical Simulation 1998年第2期 61-66页

作者： Jixiong YU (Jinhua Global Computer Engineering Co. Ltd,Jinhua 321017,China) Zhen HAN (Department of Computer, Northern JiaoTong University, Beijing, 100044, China) E mail:zhan@***

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关键词： the kdv equation difference scheme nonlinear instability conserved quantity.