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An extended(2+1)-dimensional modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation:Lax pair and Darboux transformation
《Communications in Theoretical Physics》2025年第3期12-20,共9页Li Cheng Yi Zhang Wen-Xiu Ma 
supported by the National Natural Science Foundation of China(Grant No.12271488)。
The aim of this paper is to study an extended modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff(mKdV-CBS)equation and present its Lax pair with a spectral parameter.Meanwhile,a Miura transformation is explored...
关键词：extended mKdV-CBS equation Lax pair Darboux transformation soliton solution 
(2+1)维Korteweg-de Vries-Sawada-Kotera-Ramani方程中lump波和其它非线波碰撞前后的轨迹方程
《应用数学》2025年第1期263-275,共13页黄文杰 夏亚荣 王璇 孙晓晴 
国家自然科学基金(12001424);中国博士后科学基金(2020M673332)。
本文首先基于Hirota双线性方法研究了(2+1)维Korteweg-de Vries-Sawada-Kotera-Ramani(KdVSKR)方程的多孤子解,接着利用长波极限法推导出KdVSKR方程的lump波与线波、呼吸波以及lump波的相互作用解.其次,根据lump波沿直线运动的特点,将Kd...
关键词：HIROTA双线性方法 长波极限法 轨迹方程 Lump波 
OPTIMAL ERROR ESTIMATES OF THE LOCAL DISCONTINUOUS GALERKIN METHOD WITH GENERALIZED NUMERICAL FLUXES FOR ONE-DIMENSIONAL KDV TYPE EQUATIONS
《Journal of Computational Mathematics》2025年第1期63-88,共26页Hongjuan Zhang Xiong Meng Dazhi Zhang Boying Wu 
supported by the National Natural Science Foundation of China(Grant No.11971132);by the Natural Science Foundation of Heilongjiang Province(Grant No.YQ2021A002);by the Fundamental Research Funds for the Central Universities(Grant No.HIT.OCEF.2022031);The third author was supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310006);The fourth author was supported by the National Natural Science Foundation of China(Grant Nos.11971131,61873071).
In this paper, we investigate the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear Korteweg-de Vries type equations. The numerical flux for the nonlinear convection t...
关键词：Korteweg-de Vries type equations Local discontinuous Galerkin method Generalized fluxes Error estimates 
快速衰减初值的修正Korteweg-de Vries方程的孤子解:Riemann-Hilbert方法
《应用数学学报》2024年第3期517-530,共14页杨金杰 田守富 张田田 李志强 
国家自然科学基金面上项目(12371255和11975306);徐州市基础研究计划项目(KC23048);江苏省“六大人才高峰”高层次人才项目(JY-059);中央高校基本科研业务费项目(2024ZDPYJQ1003);中国矿业大学教育教学改革研究生科研实践项目(2023YJSJG050)资助。
本文借助于Riemann-Hilbert (RH)问题研究修正Korteweg-de Vries (mKdV)方程,给出一种有效方法来获得快速衰减初值空间下的孤子解.在正散射过程建立Jost函数和散射矩阵重要性质来构建一个合适的RH问题,进而建立mKdV方程的解和RH问题解...
关键词：修正Korteweg-de Vries方程 RIEMANN-HILBERT问题 CAUCHY问题 孤子解 
Generalized Isospectral-Nonisospectral Modified Korteweg-de Vries Integrable Hierarchies and Related Properties
《Annals of Applied Mathematics》2024年第2期105-138,共34页Huanhuan Lu Xinan Ren Yufeng Zhang Hongyi Zhang 
supported by the National Natural Science Foundation of China(grant No.12371256 and No.11971475).
In this article, a new technique for deriving integrable hierarchy is discussed, i.e., such that are derived by combining the Tu scheme with the vector product. Several classes of spectral problems are introduced by t...
关键词：Darboux transformation nonlocal symmetry COVERING MANIFOLD contact structure 
New lump interaction complexitons to the(2+1)-dimensional Korteweg-de Vries equation with electrostatic wave potential in plasmas
《Journal of Ocean Engineering and Science》2024年第2期173-177,共5页Tukur Abdulkadir Sulaiman Abdullahi Yusuf Alrazi Abdeljabbar Mustafa Bayram 
A soliton is a packet of self-reinforcing waves that maintains its structure when moving at a constant speed.Solitons are caused by the cancellation of the medium’s nonlinear and dispersive effects.In plas-mas,the bi...
关键词：(2+1)-dimensional Korteweg-de Vries equation Multi waves solutions Brether waves solutions Numerical simulations 
Soliton solutions for nonlinear variable-order fractional Korteweg-de Vries(KdV)equation arising in shallow water waves
《Journal of Ocean Engineering and Science》2024年第1期50-58,共9页Umair Ali Hijaz Ahmad Hanaa Abu-Zinadah 
Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad s...
关键词：Space-time VO fractional KdV equation modified(G′/G)-expansion method VO Caputo fractional derivative generalized Riccati equation 
Korteweg-De Vries方程的Legendre时空谱配置方法
《Chinese Quarterly Journal of Mathematics》2023年第4期392-400,共9页王川 乔炎 
Supported by National Natural Science Foundation of China(Grant Nos.11771299,11371123);Natural Science Foundation of Henan Province(Grant No.202300410156).
A Legendre-Legendre spectral collocation scheme is constructed for Korteweg-de Vries(KdV)equation on bounded domain by using the Legendre collocation method in both time and space,which is a nonlinear matrix equation ...
关键词：Korteweg-de Vries equation Space-time Legendre spectral collocation method Initial-boundary value problem 
Ion-acoustic wave structures in the fluid ions modeled by higher dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation
《Journal of Ocean Engineering and Science》2023年第6期623-635,共13页U.Younas J.Ren Muhammad Z.Baber Muhammad W.Yasin T.Shahzad 
acknowledge the financial support provided for this research via Open Fund of State Key Laboratory of Power Grid Environmental Protection(No.GYW51202101374);the National Natural Science Foundation of China(52071298);Zhong Yuan Science and Technology Innovation Leadership Pro-gram(214200510010)。
In this paper,the higher dimensional generalized Korteweg-de-Varies-Zakharov-Kuznetsov(gKdV-ZK)equation is under investigation.This model is used in the field of plasma physics which describes the effects of magnetic ...
关键词：Wave solutions gKdV-ZK equation Bilinear transformation φ^(6)-model expansion method 
Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery,blood vessel or circulatory system with experimental support
《Communications in Theoretical Physics》2023年第11期49-55,共7页Xin-Yi Gao Yong-Jiang Guo Wen-Rui Shan 
supported by the National Natural Science Foundation of China under Grant Nos.11871116 and 11772017;the Fundamental Research Funds for the Central Universities of China under Grant No.2019XD-A11.
Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in,for example,variable-radius arteries.With respect to the nonlinear waves in an artery full of blood with certain aneurysm...
关键词：dynamics in blood-filled artery or blood vessel variable-coefficient generalized forced-perturbed Korteweg-de Vries-Burgers equation solitons with experimental support Bäcklund transformation and similarity reductions singular manifold 
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