Investigation of Riemann wave propagating for the variable coefficients
complicated nonlinear physical phenomena
Abstract
We are exploring solitons and other solutions describe new interaction
between two solitons besides, new three soliton solutions are generated.
we examine the commutative product between multi unknown Lie
infinitesimals for the (2+1) dimensional variable-coefficients
Bogoyavlensky Konopelchenko (VCBK) equation and this study result some
new Lie vectors. The commutative product generates a system of nonlinear
ODEs which had been solved manually. Through two stages of Lie symmetry
reduction, (VCBK) equation is reduced to non-solvable nonlinear ODEs
using various combinations of optimal Lie vectors. Using the Integration
method, we investigate new analytical solutions for these ODEs. Back
substituting to the original variables generates new solitons and other
solutions for (VCBK). Some selected solutions illustrated through
three-dimensional plots.