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, t...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.展开更多
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
<Abstract>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 sing...<Abstract>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 finite- amplitude 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
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
In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped fibre.The determinant re...In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped fibre.The determinant representation of Darboux transformation is used to derive soliton solutions,positon solutions to the IH-MB equations.展开更多
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China under Grant No.10601028
文摘<Abstract>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 finite- amplitude 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.
基金Supported by the Nationai Basic Research Program of China (973 program) under Grant No. 2007CB814800the National Science Foundation of China under Grant Nos. 10801083 and 10901090
文摘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.
基金Supported by the Key Project of Chinese Ministry of Education under Grant No 106033, the National Natural Science Foundation of China under Grant Nos 60372095 and 60772023, Open Fund of the State Key Laboratory of Software Development Environment under Grant No SKLSDE-07-001, Beijing University of Aeronautics and Astronautics, the National Basic Research Programme of China under Grant No 2005CB321901, the Green Path Programme of Air Force of the Chinese People＇s Liberation Army, the Cheung Kong Scholars Programme of the Ministry of Education of China and Li Ka Shing Foundation of Hong Kong.
基金supported by the National Natural Science Foundation of China(Grant Nos.11201251 and 11271210)Zhejiang Provincial Natural Science Foundation of China(Grant No.LY12A01007)+1 种基金the Natural Science Foundation of Ningbo(Grant No.2013A610105)K.C.Wong Magna Fund in Ningbo University
文摘In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped fibre.The determinant representation of Darboux transformation is used to derive soliton solutions,positon solutions to the IH-MB equations.
