Lie symmetries, optimal system, group-invariant solutions and dynamical behaviors of solitary wave solutions for a (3+1)-dimensional KdV-type equation
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, 110007, Delhi, India
2 SGTB Khalsa College, University of Delhi, 110007, Delhi, India
3 Department of Mathematics, Saint Xavier University, 60655, Chicago, IL, USA
Accepted: 4 May 2021
Published online: 13 May 2021
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility by the properties of nonlinear hydrodynamics. In this present work, numerous group-invariant solutions of the (3+1)-dimensional KdV-type equation are derived with the virtue of Lie symmetry analysis. Also, we obtain the corresponding infinitesimal generators, Lie point symmetries, geometric vector fields, commutator table and a one-dimensional optimal system of subalgebras. In addition, two-dimensional optimal system of subalgebra is also obtained using one-dimensional optimal system. Several interesting symmetry reductions and corresponding group-invariant solutions of the equation are obtained based on a one-dimensional optimal system of subalgebras. These group-invariant solutions include special functions like the WeierstrassZeta function, W-shaped solitons, M-shaped solitons, bright-dark solitons, solitary waves and rogue waves which we furnish for the first time for this equation. The physical interpretation of the obtained solutions is discussed graphically based on numerical simulation through Mathematica. Furthermore, nonlocal conservation laws are studied via the Ibragimov approach for Lie point symmetries.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021