The Logarithmic (1+1)-Dimensional KdV-Like and (2+1)-Dimensional KP-Like Equations: Lie Group Analysis, Conservation Laws and Double Reductions

Abstract

We investigate the logarithmic (1 + 1) dimensional KdV-like and (2 + 1) dimensional KP-like equations which model many physical processes in the field of soliton theory. In this paper, first, we get the classical Lie point symmetries using the invariance theory. Secondly, we obtain conservation laws of the underlying equations by incorporating the method of multiplier and non-local conservation method. A relationship between the obtained symmetries and conservation laws are shown. Then using the generalized double reduction theory for the associated symmetries, reductions are constructed. Finally traveling wave solutions are computed with the aid of the simplest equation method for the logarithmic (2 + 1)-dimensional KP-like equation.