Solving nonlinear partial differential equations have attracted intensive attention in the past few decades.In this paper,the Darboux transformation method is used to derive several positon and hybrid solutions for th...Solving nonlinear partial differential equations have attracted intensive attention in the past few decades.In this paper,the Darboux transformation method is used to derive several positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg–de Vries equations.Based on the zero seed solution,the positon solution and the hybrid solutions of positon and soliton are constructed.The composition of positons is studied,showing that multi-positons of(2+1)-dimensional equations are decomposed into multi-solitons as well as the(1+1)-dimensions.Moreover,the interactions between positon and soliton are analyzed.In addition,the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution,and their evolutions with time are discussed.展开更多
In this letter,we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation over a nonzero background.First,we obtain 2 n-soliton solutions with a nonzero ba...In this letter,we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation over a nonzero background.First,we obtain 2 n-soliton solutions with a nonzero background via n-fold Darboux transformation,and find that these soliton solutions will appear in pairs.Particularly,2 n-soliton solutions consist of n‘bright’solitons and n‘dark’solitons.This phenomenon implies a new form of integrability:even integrability.Then interactions between solitons with even numbers and breathers are studied in detail.To our best knowledge,a novel nonlinear superposition between a kink and 2 n-soliton is also generated for the first time.Finally,interactions between some different smooth positons with a nonzero background are derived.展开更多
Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries （KdV） equation, we prove that the variable-coeFficient KdV equation under the Painlevé test...Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries （KdV） equation, we prove that the variable-coeFficient KdV equation under the Painlevé test condition also possesses the formal conservation laws.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
基金Project sponsored by NUPTSF(Grant Nos.NY220161and NY222169)the Foundation of Jiangsu Provincial Double-Innovation Doctor Program(Grant No.JSSCBS20210541)+1 种基金the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,China(Grant No.22KJB110004)the National Natural Science Foundation of China(Grant No.11871446)。
文摘Solving nonlinear partial differential equations have attracted intensive attention in the past few decades.In this paper,the Darboux transformation method is used to derive several positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg–de Vries equations.Based on the zero seed solution,the positon solution and the hybrid solutions of positon and soliton are constructed.The composition of positons is studied,showing that multi-positons of(2+1)-dimensional equations are decomposed into multi-solitons as well as the(1+1)-dimensions.Moreover,the interactions between positon and soliton are analyzed.In addition,the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution,and their evolutions with time are discussed.
基金supported by National Natural Science Foundation of China under Grant Nos.11775121K C Wong Magna Fund in Ningbo University。
文摘In this letter,we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation over a nonzero background.First,we obtain 2 n-soliton solutions with a nonzero background via n-fold Darboux transformation,and find that these soliton solutions will appear in pairs.Particularly,2 n-soliton solutions consist of n‘bright’solitons and n‘dark’solitons.This phenomenon implies a new form of integrability:even integrability.Then interactions between solitons with even numbers and breathers are studied in detail.To our best knowledge,a novel nonlinear superposition between a kink and 2 n-soliton is also generated for the first time.Finally,interactions between some different smooth positons with a nonzero background are derived.
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.
文摘Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries （KdV） equation, we prove that the variable-coeFficient KdV equation under the Painlevé test condition also possesses the formal conservation laws.
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.
