A generalized Drinfel＇d Sokolov-Wilson （DSW） equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spect...A generalized Drinfel＇d Sokolov-Wilson （DSW） equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spectral problems, from which a Darboux transformation for the DSW equation is obtained through a reduction technique. As an application of the Darboux transformations, we give some explicit solutions of the generalized DSW equation and DEW equation such as rational solutions, soliton solutions, periodic solutions.展开更多
In this paper, an extended method is proposed for constructing new forms of exact travelling wave solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we app...In this paper, an extended method is proposed for constructing new forms of exact travelling wave solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to the asymmetric Nizhnik-Novikov-Vesselov equation and the coupled Drinfel＇d-Sokolov-Wilson equation and successfully cover the previously known travelling wave solutions found by Chen＇s method .展开更多
The system of(1+1)-coupled Drinfel’d-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the seabed.The objective of the present research is to construct a new variety of analytica...The system of(1+1)-coupled Drinfel’d-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the seabed.The objective of the present research is to construct a new variety of analytical solutions for the system.The invariants are derived with the aid of Killing form by using the optimal algebra classification via Lie symmetry approach.The invariant solutions involve time,space variables,and arbitrary constants.Imposing adequate constraints on arbitrary constants,solutions are represented graphically to make them more applicable in designing sea models.The behavior of solutions shows asymptotic,bell-shaped,bright and dark soliton,bright soliton,parabolic,bright and kink,kink,and periodic nature.The constructed results are novel as the reported results[26,28,29,30,33,38,42,49]can be deduced from the results derived in this study.The remaining solutions derived in this study,are absolutely different from the earlier findings.In this study,the physical character of analytical solutions of the system could aid coastal engineers in creating models of beaches and ports.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Supported by National Natural Science Foundation of China under Grant No.10871182Innovation Scientists and Technicians Troop Construction Projects of Henan Province
文摘A generalized Drinfel＇d Sokolov-Wilson （DSW） equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spectral problems, from which a Darboux transformation for the DSW equation is obtained through a reduction technique. As an application of the Darboux transformations, we give some explicit solutions of the generalized DSW equation and DEW equation such as rational solutions, soliton solutions, periodic solutions.
文摘In this paper, an extended method is proposed for constructing new forms of exact travelling wave solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to the asymmetric Nizhnik-Novikov-Vesselov equation and the coupled Drinfel＇d-Sokolov-Wilson equation and successfully cover the previously known travelling wave solutions found by Chen＇s method .
文摘The system of(1+1)-coupled Drinfel’d-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the seabed.The objective of the present research is to construct a new variety of analytical solutions for the system.The invariants are derived with the aid of Killing form by using the optimal algebra classification via Lie symmetry approach.The invariant solutions involve time,space variables,and arbitrary constants.Imposing adequate constraints on arbitrary constants,solutions are represented graphically to make them more applicable in designing sea models.The behavior of solutions shows asymptotic,bell-shaped,bright and dark soliton,bright soliton,parabolic,bright and kink,kink,and periodic nature.The constructed results are novel as the reported results[26,28,29,30,33,38,42,49]can be deduced from the results derived in this study.The remaining solutions derived in this study,are absolutely different from the earlier findings.In this study,the physical character of analytical solutions of the system could aid coastal engineers in creating models of beaches and ports.
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.
