These rational solutions which can be described a kind of algebraic solitary waves which have great potential in applied value in atmosphere and ocean. It has attracted more and more attention recently. In this paper,...These rational solutions which can be described a kind of algebraic solitary waves which have great potential in applied value in atmosphere and ocean. It has attracted more and more attention recently. In this paper, the generalized bilinear method instead of the Hirota bilinear method is used to obtain the rational solutions to the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli-like equation (hereinafter referred to as BLMP equation). Meanwhile, the (2 + 1)-dimensional BLMP-like equation is derived on the basis of the generalized bilinear operators D3,x D3,y and D3,t. And the rational solutions to the (2 + 1)-dimensional BLMP-like equation are obtained successively. Finally, with the help of the N-soliton solutions of the (2 + 1)-dimensional BLMP equation, the interactions of the N-soliton solutions can be derived. The results show that the two soliton still maintained the original waveform after happened collision.展开更多
This paper is devoted to the study of a (2 + 1)-dimensional extended Potential Boiti-Leon-Manna-Pempinelli equation. Firstly, By means of the standard Weiss Tabor Carnevale approach and Kruskal’s simplification, we p...This paper is devoted to the study of a (2 + 1)-dimensional extended Potential Boiti-Leon-Manna-Pempinelli equation. Firstly, By means of the standard Weiss Tabor Carnevale approach and Kruskal’s simplification, we prove the painlevé non integrability of the equation. Secondly, A new breather solution and lump type solution are obtained based on the parameter limit method and Hirota’s bilinear method. Besides, some interaction behavior between lump type solution and N-soliton solutions (N is any positive integer) are studied. We construct the existence theorem of the interaction solution and give the process of calculation and proof. We also give a concrete example to illustrate the effectiveness of the theorem, and some spatial structure figures are displayed to reflect the evolutionary behavior of the interaction solutions with the change of soliton number N and time t.展开更多
<正> In this short note,a new projective equation(φ′=σφ+φ~2)is used to obtain the variable separationsolutions with two arbitrary functions of the(2+1)-dimensional Boiti-Leon-Manna-Pempinelli system(BLMP).B...<正> In this short note,a new projective equation(φ′=σφ+φ~2)is used to obtain the variable separationsolutions with two arbitrary functions of the(2+1)-dimensional Boiti-Leon-Manna-Pempinelli system(BLMP).Basedon the derived solitary wave solution and by selecting appropriate functions,some novel localized excitations such asmulti dromion-solitoffs and fractal-solitons are investigated.展开更多
In this paper,multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli(BLMP) equation by using Hirota bilinear method and Riemann theta function.At the same time,weanalyze in ...In this paper,multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli(BLMP) equation by using Hirota bilinear method and Riemann theta function.At the same time,weanalyze in details asymptotic properties of the multi-periodic wave solutions and give their asymptotic relations betweenthe periodic wave solutions and the soliton solutions.展开更多
文摘These rational solutions which can be described a kind of algebraic solitary waves which have great potential in applied value in atmosphere and ocean. It has attracted more and more attention recently. In this paper, the generalized bilinear method instead of the Hirota bilinear method is used to obtain the rational solutions to the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli-like equation (hereinafter referred to as BLMP equation). Meanwhile, the (2 + 1)-dimensional BLMP-like equation is derived on the basis of the generalized bilinear operators D3,x D3,y and D3,t. And the rational solutions to the (2 + 1)-dimensional BLMP-like equation are obtained successively. Finally, with the help of the N-soliton solutions of the (2 + 1)-dimensional BLMP equation, the interactions of the N-soliton solutions can be derived. The results show that the two soliton still maintained the original waveform after happened collision.
文摘This paper is devoted to the study of a (2 + 1)-dimensional extended Potential Boiti-Leon-Manna-Pempinelli equation. Firstly, By means of the standard Weiss Tabor Carnevale approach and Kruskal’s simplification, we prove the painlevé non integrability of the equation. Secondly, A new breather solution and lump type solution are obtained based on the parameter limit method and Hirota’s bilinear method. Besides, some interaction behavior between lump type solution and N-soliton solutions (N is any positive integer) are studied. We construct the existence theorem of the interaction solution and give the process of calculation and proof. We also give a concrete example to illustrate the effectiveness of the theorem, and some spatial structure figures are displayed to reflect the evolutionary behavior of the interaction solutions with the change of soliton number N and time t.
基金Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606128the Scientific Research Fund of Zhejiang Provincial Education Department of China under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant Nos.KZ08001 and KZ09005
文摘<正> In this short note,a new projective equation(φ′=σφ+φ~2)is used to obtain the variable separationsolutions with two arbitrary functions of the(2+1)-dimensional Boiti-Leon-Manna-Pempinelli system(BLMP).Basedon the derived solitary wave solution and by selecting appropriate functions,some novel localized excitations such asmulti dromion-solitoffs and fractal-solitons are investigated.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1412800 the Innovation Program of Shanghai Municipal Education Commission under Grant No.10ZZ131
文摘In this paper,multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli(BLMP) equation by using Hirota bilinear method and Riemann theta function.At the same time,weanalyze in details asymptotic properties of the multi-periodic wave solutions and give their asymptotic relations betweenthe periodic wave solutions and the soliton solutions.
