We investigate and concentrate on new infinitesimal generators of Lie symmetries for an extended(2+1)-dimensional Calogero-Bogoyavlenskii-Schif(eCBS)equation using the commutator table which results in a system of non...We investigate and concentrate on new infinitesimal generators of Lie symmetries for an extended(2+1)-dimensional Calogero-Bogoyavlenskii-Schif(eCBS)equation using the commutator table which results in a system of nonlinear ordinary differential equations(ODEs)which can be manually solved.Through two stages of Lie symmetry reductions,the eCBS equation is reduced to non-solvable nonlinear ODEs using different combinations of optimal Lie vectors.Using the integration method and the Riccati and Bernoulli equation methods,we investigate new analytical solutions to those ODEs.Back substituting to the original variables generates new solutions to the eCBS equation.These results are simulated through three-and two-dimensional plots.展开更多
This work aims to present nonlinear models that arise in ocean engineering.There are many models of ocean waves that are present in nature.In shallow water,the linearization of the equations requires critical conditio...This work aims to present nonlinear models that arise in ocean engineering.There are many models of ocean waves that are present in nature.In shallow water,the linearization of the equations requires critical conditions on wave capacity than it make in deep water,and the strong nonlinear belongings are spotted.We use Lie symmetry analysis to obtain different types of soliton solutions like one,two,and three-soliton solutions in a(2+1)dimensional variable-coefficient Bogoyavlensky Konopelchenko(VCBK)equation that describes the interaction of a Riemann wave reproducing along the y-axis and a long wave reproducing along the x-axis in engineering and science.We use the Lie symmetry analysis then the integrating factor method to obtain new solutions of the VCBK equation.To demonstrate the physical meaning of the solutions obtained by the presented techniques,the graphical performance has been demonstrated with some values.The presented equation has fewer dimensions and is reduced to ordinary differential equations using the Lie symmetry technique.展开更多
文摘We investigate and concentrate on new infinitesimal generators of Lie symmetries for an extended(2+1)-dimensional Calogero-Bogoyavlenskii-Schif(eCBS)equation using the commutator table which results in a system of nonlinear ordinary differential equations(ODEs)which can be manually solved.Through two stages of Lie symmetry reductions,the eCBS equation is reduced to non-solvable nonlinear ODEs using different combinations of optimal Lie vectors.Using the integration method and the Riccati and Bernoulli equation methods,we investigate new analytical solutions to those ODEs.Back substituting to the original variables generates new solutions to the eCBS equation.These results are simulated through three-and two-dimensional plots.
文摘This work aims to present nonlinear models that arise in ocean engineering.There are many models of ocean waves that are present in nature.In shallow water,the linearization of the equations requires critical conditions on wave capacity than it make in deep water,and the strong nonlinear belongings are spotted.We use Lie symmetry analysis to obtain different types of soliton solutions like one,two,and three-soliton solutions in a(2+1)dimensional variable-coefficient Bogoyavlensky Konopelchenko(VCBK)equation that describes the interaction of a Riemann wave reproducing along the y-axis and a long wave reproducing along the x-axis in engineering and science.We use the Lie symmetry analysis then the integrating factor method to obtain new solutions of the VCBK equation.To demonstrate the physical meaning of the solutions obtained by the presented techniques,the graphical performance has been demonstrated with some values.The presented equation has fewer dimensions and is reduced to ordinary differential equations using the Lie symmetry technique.
