In this study,we investigate the(2+1)-dimensional Korteweg-De Vries(KdV)equation with the extension of time-dependent coefficients.A symbolic computational method,the simplified Hirota’s method,and a long-wave method...In this study,we investigate the(2+1)-dimensional Korteweg-De Vries(KdV)equation with the extension of time-dependent coefficients.A symbolic computational method,the simplified Hirota’s method,and a long-wave method are utilized to create various exact solutions to the suggested equation.The symbolic computational method is applied to create the Lump solutions and periodic lump waves.Hirota’s method and a long-wave method are implemented to explore single-,double-and triple-M-lump waves,and interaction physical phenomena such as an interaction of single-M-lump with one-,twosoliton solutions,as well as a collision of double-M-lump with single-soliton waves.Furthermore,the simplified Hirota’s method is employed to explore complex multi-soliton solutions.To realize dynamics,the gained solutions are drawn via utilizing different arbitrary variable coefficients.展开更多
In this work,we use the(m+1/G')-expansion method and the Adomian decomposition method to study the 3D potential Yu-Toda-Sasa-Fukuyama(3D-pYTSF)equation which has a good application in the twolayer liquid medium.Fo...In this work,we use the(m+1/G')-expansion method and the Adomian decomposition method to study the 3D potential Yu-Toda-Sasa-Fukuyama(3D-pYTSF)equation which has a good application in the twolayer liquid medium.For the first time,the(m+1/G')-expansion and the Adomian decomposition methods are used to establish novel exact wave solutions and to study some numerical solutions for the 3D-pYTSF equation,respectively.Through using the analytical method,kink-type wave,singular solution and some complex solutions to the suggested equation are successfully revealed.The obtained wave solutions are represented with some figures in 3D and contour plots.展开更多
文摘In this study,we investigate the(2+1)-dimensional Korteweg-De Vries(KdV)equation with the extension of time-dependent coefficients.A symbolic computational method,the simplified Hirota’s method,and a long-wave method are utilized to create various exact solutions to the suggested equation.The symbolic computational method is applied to create the Lump solutions and periodic lump waves.Hirota’s method and a long-wave method are implemented to explore single-,double-and triple-M-lump waves,and interaction physical phenomena such as an interaction of single-M-lump with one-,twosoliton solutions,as well as a collision of double-M-lump with single-soliton waves.Furthermore,the simplified Hirota’s method is employed to explore complex multi-soliton solutions.To realize dynamics,the gained solutions are drawn via utilizing different arbitrary variable coefficients.
基金Deanship of Scientific Re-search at Umm Al-Qura University for supporting this work by Grant Code:(22UQU4410172DSR06).
文摘In this work,we use the(m+1/G')-expansion method and the Adomian decomposition method to study the 3D potential Yu-Toda-Sasa-Fukuyama(3D-pYTSF)equation which has a good application in the twolayer liquid medium.For the first time,the(m+1/G')-expansion and the Adomian decomposition methods are used to establish novel exact wave solutions and to study some numerical solutions for the 3D-pYTSF equation,respectively.Through using the analytical method,kink-type wave,singular solution and some complex solutions to the suggested equation are successfully revealed.The obtained wave solutions are represented with some figures in 3D and contour plots.
