This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model.Thus,we acquire some two-wave and breather wave solutions to the governing equation.Breathers are pulsating localized struc...The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model.Thus,we acquire some two-wave and breather wave solutions to the governing equation.Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process.Several recent investigations,on the other hand,imply that breathers can survive in more complex habitats,such as random seas,despite the attributed physical restrictions.The authenticity and genuineness of all the acquired solutions agreed with the original equation.In order to shed more light on these novel solutions,we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values.The governing model is also stable because of the idea of linear stability.The study’s findings may help explain the physics behind some of the challenges facing ocean engineers.展开更多
We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.Th...We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.The N-soliton, N-breather and N th-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first-to second-order ones are shown.展开更多
The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,co...The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,coastal engineering,fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound waves.In this paper,this equation is investigated and analyzed using two effective schemes.The well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under consideration.The breather wave solutions are derived using the Cole–Hopf transformation.In addition,by means of new conservation theorem,we construct conservation laws(CLs)for the governing equation by means of Lie–Bäcklund symmetries.The novel characteristics for the(2+1)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
文摘The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model.Thus,we acquire some two-wave and breather wave solutions to the governing equation.Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process.Several recent investigations,on the other hand,imply that breathers can survive in more complex habitats,such as random seas,despite the attributed physical restrictions.The authenticity and genuineness of all the acquired solutions agreed with the original equation.In order to shed more light on these novel solutions,we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values.The governing model is also stable because of the idea of linear stability.The study’s findings may help explain the physics behind some of the challenges facing ocean engineers.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11705290 and 11305060the China Postdoctoral Science Foundation under Grant No 2016M602252
文摘We derive an N-fold Darboux transformation for the nonlinear Schrdinger equation coupled to a multiple selfinduced transparency system, which is applicable to optical fiber communications in the erbium-doped medium.The N-soliton, N-breather and N th-order rogue wave solutions in the compact determinant representations are derived using the Darboux transformation and limit technique. Dynamics of such solutions from the first-to second-order ones are shown.
文摘The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,coastal engineering,fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound waves.In this paper,this equation is investigated and analyzed using two effective schemes.The well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under consideration.The breather wave solutions are derived using the Cole–Hopf transformation.In addition,by means of new conservation theorem,we construct conservation laws(CLs)for the governing equation by means of Lie–Bäcklund symmetries.The novel characteristics for the(2+1)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.