In this paper, an explicit Bgcklund transformation （BT） of the Burgers equation is obtained by using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669]. Ba...In this paper, an explicit Bgcklund transformation （BT） of the Burgers equation is obtained by using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669]. Based on the BT and some newly obtained seed solutions, infinite sequences of exact solutions for the Burgers equation are generated. Further more, this BT of the Burgers equation is applied to solve the variant Boussinesq equations and the approximate equations of long water wave.展开更多
In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are ...In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are also proposed/or this model.展开更多
Variable separation approach that is based on Baeicklund transformation （BT-VSA） is extended to solve the （3＋1）-dimensional Jimbo- Miwa equation and the （1＋1）-dimensional Drinfel＇d-Sokolov Wilson equation. Ne...Variable separation approach that is based on Baeicklund transformation （BT-VSA） is extended to solve the （3＋1）-dimensional Jimbo- Miwa equation and the （1＋1）-dimensional Drinfel＇d-Sokolov Wilson equation. New exact solutions, which include some low-dimensional functions, are obtained. One of the low-dimensional function is arbitrary and another must satisfy a Riccati equation. Some new localized excitations can be derived from （2＋1）-dimensional localized excitations and for simplification, we omit those in this letter.展开更多
基金中国博士后科学基金，国家重点基础研究发展计划(973计划)，the National Key Basic Research Project of China under
文摘In this paper, an explicit Bgcklund transformation （BT） of the Burgers equation is obtained by using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669]. Based on the BT and some newly obtained seed solutions, infinite sequences of exact solutions for the Burgers equation are generated. Further more, this BT of the Burgers equation is applied to solve the variant Boussinesq equations and the approximate equations of long water wave.
基金The project supported by National Natural Science Foundation of China under Grant No. 90203001, the Fund of the State Key Laboratory of Scientific and Engineering Computing, the Chinese Academy of Sciences, and Hong Kong Research Grant Council under Grant No. HKBU/2016/03P
文摘In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are also proposed/or this model.
基金The author is very gruteful to referees for all kinds of help.
文摘Variable separation approach that is based on Baeicklund transformation （BT-VSA） is extended to solve the （3＋1）-dimensional Jimbo- Miwa equation and the （1＋1）-dimensional Drinfel＇d-Sokolov Wilson equation. New exact solutions, which include some low-dimensional functions, are obtained. One of the low-dimensional function is arbitrary and another must satisfy a Riccati equation. Some new localized excitations can be derived from （2＋1）-dimensional localized excitations and for simplification, we omit those in this letter.
