2 research outputs found
1-Multisoliton and other invariant solutions of combined KdV - nKdV equation by using symmetry approach
Lie symmetry method is applied to investigate symmetries of the combined
KdV-nKdV equation, that is a new integrable equation by combining the KdV
equation and negative order KdV equation. Symmetries which are obtained in this
article, are further helpful for reducing the combined KdV-nKdV equation into
ordinary differential equation. Moreover, a set of eight invariant solutions
for combined KdV-nKdV equation is obtained by using proposed method. Out of the
eight solutions so obtained in which two solutions generate progressive wave
solutions, five are singular solutions and one multisoliton solutions which is
in terms of WeierstrassZeta function.Comment: 11 Pages, 12 figures, Original Research Articl
New solitary wave and Multiple soliton solutions of (3 + 1)-dimensional KdV type equation by using Lie symmetry approach
Solitary waves are localized gravity waves that preserve their consistency
and henceforth their visibility through properties of nonlinear hydrodynamics.
Solitary waves have finite amplitude and spread with constant speed and
constant shape. In this paper, we have used Lie group of transformation method
to solve (3 + 1)-dimensional KdV type equation. We have obtained the
infinitesimal generators, commutator table of Lie algebra for the KdV type
equation. We have achieved a number of exact solutions of KdV type equation in
the explicit form through similarity reduction. All the reported results are
expressed in analytic (closed form) and figured out graphically through their
evolution solution profiles. We characterized the physical explanation of the
obtained solutions with the free choice of the particular parameters by
plotting some 3D and 2D illustrations. The geometrical analysis explains that
the nature of solutions is travelling wave, kink wave, single solitons, doubly
solitons and curve-shaped multisolitons.Comment: 22 pages, 19 figure