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Nonsingular positon Solutions of a Variable-Coefficient Modified KdV Equation

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Open Journal of Applied Sciences 2013年第1期3卷 102-105页

作者： Yi Lin Chuanzhong Li Jingsong He Department of Mathematics Ningbo University Ningbo China

The determinant representation of three-fold Darboux transformation for a variable-coefficient modified KdV equation is displayed based on the technique used to solve Ablowitz-Kaup-Newell-Segur system. Additionally, the nonsingular positon solutions of the variable-coefficient modified KdV equation are firstly discovered analytically and graphically.

关键词： Variable-Coefficient KdV Equation Lax Pair Darboux Transformation positon Soliton-positon

Dynamics of the Smooth positons of the Wadati-Konno-Ichikawa Equation

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Communications in Theoretical Physics 2018年第3期69卷 227-232页

作者： Gai-Hua Wang Yong-Shuai Zhang Jing-Song He Department of Mathematics Ningbo UniversityNingbo 315211China School of Science Zhejiang University of Science and TechnologyHangzhou 310023China

We discuss a modified Wadati-Konno-Ichikawa(m WKI)equation,which is equivalent to the WKI equation by a hodograph *** explicit formula of degenerated solution of m WKI equation is provided by using degenerate Darboux transformation with respect to the eigenvalues,which yields two kinds of smooth solutions possessing the vanishing and nonvanishing boundary conditions *** particular,a method for the decomposition of modulus square is operated to the positon solution,and the approximate orbits before and after collision of positon solutions are displayed explicitly.

关键词： Wadati-Konno-Ichikawa equation positon breather-positon trajectory phase shift

Smooth positons of the Second-Type Derivative Nonlinear Schr?dinger Equation

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Communications in Theoretical Physics 2019年第4期71卷 357-361页

作者： Shu-Zhi Liu Yong-Shuai Zhang Jing-Song He Department of Mathematics Ningbo University School of Science Zhejiang University of Science and Technology

We construct the soliton solution and smooth positon solution of the second-type derivative nonlinear Schr¨odinger(DNLSII) equation. Additionally, we present a detailed discussion about the decomposition of the positon solution, and display its approximate orbits and variable "phase shift". The second and third order breather-positon solutions are also constructed.

关键词： Chen-Lee-Liu equation positon breather-positon Daroboux transformation

On Camassa-Holm Equation with Self-Consistent Sources and Its Solutions

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Communications in Theoretical Physics 2010年第3期53卷 403-412页

作者：黄晔辉姚玉芹曾云波 Department of Mathematical Science Tsinghua University Department of Applied Mathematics China Agricultural University

Regarded as the integrable generalization of Camassa-Holm (CH) equation, the CH equation with selfconsistent sources (CHESCS) is derived. The Lax representation of the CHESCS is presented. The conservation laws for CHESCS are constructed. The peakon solution, N-soliton, N-cuspon, N-positon, and N-negaton solutions of CHESCS are obtained by using Darboux transformation and the method of variation of constants.

关键词： Camassa Holm equation with self-consistent sources Lax representation conservation laws peakon soliton positon negaton

On Coupled KdV Equations with Self-consistent Sources

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Communications in Theoretical Physics 2008年第5期49卷 1091-1100页

作者： HUANG Ye-Hui WU Hong-Xia XIE Xi ZENG Yun-Bo Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics School of Science Jimei University Xiamen 361021 China

The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.

关键词： coupled KdV equation with self-consistent sources generalized binary Darboux transformation positon negaton complexiton

Wronskian Determinant Solutions for the (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation

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Journal of Applied Mathematics and Physics 2013年第5期1卷 18-24页

作者： Hongcai Ma Yongbin Bai Department of Applied Mathematics Donghua University Shanghai China

In this paper, we consider (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Based on the bilinear form, we derive exact solutions of (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation by using th... 详细信息

关键词： (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation The Wronskian Technique Soliton Negaton positon