| 1 | Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles for a (2+1)-dimensional weakly coupled B-Type Kadomtsev-Petviashvili equations显示文摘In the case of negligible viscosity and surface tension,the B-KP equation shows the evolution of quasione-dimensional shallow-water waves,and it is growingly used in ocean physics,marine engineering,plasma physics,optical fibers,surface and internal oceanic waves,Bose-Einstein condensation,ferromagnetics,and string theory.Due to their importance and applications,many features and characteristics have been investigated.In this work,we attempt to perform Lie symmetry reductions and closed-form solutions to the weakly coupled B-Type Kadomtsev-Petviashvili equation using the Lie classical method.First,an optimal system based on one-dimensional subalgebras is constructed,and then all possible geometric vector yields are achieved.We can reduce system order by employing the one-dimensional optimal system.Furthermore,similarity reductions and exact solutions of the reduced equations,which include arbitrary independent functional parameters,have been derived.These newly established solutions can enhance our understanding of different nonlinear wave phenomena and dynamics.Several threedimensional and two-dimensional graphical representations are used to determine the visual impact of the produced solutions with determined parameters to demonstrate their dynamical wave profiles for various examples of Lie symmetries.Various new solitary waves,kink waves,multiple solitons,stripe soliton,and singular waveforms,as well as their propagation,have been demonstrated for the weakly coupled B-Type Kadomtsev-Petviashvili equation.Lie classical method is thus a powerful,robust,and fundamental scientific tool for dealing with NPDEs.Computational simulations are also used to prove the effectiveness of the proposed approach. | Setu Rani Sachin Kumar Raj Kumar | 2023 | Journal of Ocean Engineering and Science2023，8，2： | 0 |
| 2 | Study of exact analytical solutions and various wave profiles of a new extended(2+1)-dimensional Boussinesq equation using symmetry analysis显示文摘This paper systematically investigates the exact solutions to an extended(2+1)-dimensional Boussinesq equation,which arises in several physical applications,including the propagation of shallow-water waves,with the help of the Lie symmetry analysis method.We acquired the vector fields,commutation relations,optimal systems,two stages of reductions,and exact solutions to the given equation by taking advantage of the Lie group method.The method plays a crucial role to reduce the number of independent variables by one in each stage and finally forms an ODE which is solved by taking relevant suppositions and choosing the arbitrary constants that appear therein.Furthermore,Lie symmetry analysis(LSA)is implemented for perceiving the symmetries of the Boussinesq equation and then culminating the solitary wave solutions.The behavior of the obtained results for multiple cases of symmetries is obtained in the present framework and demonstrated through three-and two-dimensional dynamical wave profiles.These solutions show single soliton,multiple solitons,elastic behavior of combo soliton profiles,and stationary waves,as can be seen from the graphics.The outcomes of the present investigation manifest that the considered scheme is systematic and significant to solve nonlinear evolution equations. | Sachin Kumar Setu Rani | 2022 | Journal of Ocean Engineering and Science2022，7，5： | 0 |
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