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Soliton, Positon and Negaton Solutions of Extended KdV Equation
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作者 WU Hong-Xia ZENG Yun-Bo FAN Tian-You 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第3期529-534,共6页
Darboux transformation (DT) provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV (eKdV) equation, by which some new solutions such as singular solito... Darboux transformation (DT) provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV (eKdV) equation, by which some new solutions such as singular soliton, negaton, and positon solutions are computed for the eKdV equation. We rediscover the soliton solution with finiteamplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys. 89 (1999) 173] and discuss the difference between this soliton and the singular soliton. We clarify the relationship between the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail. 展开更多
关键词 the extended KdV equation singular soliton POSITON negaton Darboux transformation
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Negatons, Positons, and Complexiton Solutions of Higher Order for a Non-isospectral KdV Equation
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作者 ZHANG Yuan-Yuan WANG Qi ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第3X期411-414,共4页
In this paper, negatons, positons, and complexiton solutions of higher order for a non-isospectral KdV equation, the KdV equation with loss and non-uniformity terms are obtained through the bilinear Baicklund transfor... In this paper, negatons, positons, and complexiton solutions of higher order for a non-isospectral KdV equation, the KdV equation with loss and non-uniformity terms are obtained through the bilinear Baicklund transformation. Further, the properties of some solutions are shown by some figures made by using Maple. 展开更多
关键词 bilinear Backlund transformation negatons positons complexiton solutions
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耦合mKdV系统的非奇异正子解、负子解及复子解 被引量:4
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作者 张玲 桑本文 胡恒春 《上海理工大学学报》 CAS 北大核心 2012年第1期76-80,87,共6页
研究从二层流体模型中导出的变系数耦合mKdV模型,利用达布变换法,并依据系统中Lax对的谱参数的性质,给出了耦合mKdV系统的正子解、负子解、复子解及这些解的具体结构图形.其中所得到的耦合mKdV系统的正子解、负子解和复子解都是解析的,... 研究从二层流体模型中导出的变系数耦合mKdV模型,利用达布变换法,并依据系统中Lax对的谱参数的性质,给出了耦合mKdV系统的正子解、负子解、复子解及这些解的具体结构图形.其中所得到的耦合mKdV系统的正子解、负子解和复子解都是解析的,而复子解可看作一种形式的周期波解. 展开更多
关键词 正子解 负子解 复子解 耦合KdV系统
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On Coupled KdV Equations with Self-consistent Sources 被引量:2
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作者 HUANG Ye-Hui WU Hong-Xia +1 位作者 XIE Xi ZENG Yun-Bo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第5期1091-1100,共10页
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-... 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. 展开更多
关键词 coupled KdV equation with self-consistent sources generalized binary Darboux transformation POSITON negaton COMPLEXITON
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Wronskian Determinant Solutions for the (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation 被引量:1
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作者 Hongcai Ma Yongbin Bai 《Journal of Applied Mathematics and Physics》 2013年第5期18-24,共7页
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... 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 the Wronskian technique, which include rational solutions, soliton solutions, positons and negatons. 展开更多
关键词 (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli EQUATION The WRONSKIAN Technique Soliton negaton Positon
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On Camassa-Holm Equation with Self-Consistent Sources and Its Solutions
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作者 黄晔辉 姚玉芹 曾云波 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期403-412,共10页
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 CH... 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. 展开更多
关键词 Camassa Holm equation with self-consistent sources Lax representation conservation laws PEAKON SOLITON POSITON negaton
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