Reciprocal Bäcklund transformations and travelling wave structures of some nonlinear pseudo-parabolic equations

Abstract

The equations in which time derivative appears in the highest order derivative term are called pseudo-parabolic equations. In this article, we will propose new singular and dark soliton solutions to a few such equations. We first find the symmetry algebra of such equations, and then by invariant reduction we obtain the exact solutions. Then, we classify the solutions by using their Lie subalgebras. Also, we will discuss the travelling wave solutions by using tanh–coth method. Moreover, we will discuss reciprocal Bäcklund transformations of the conservation laws.

Keywords

• Pseudo-parabolic equations
• Symmetry algebra
• Travelling wave solutions
• Reciprocal Bäcklund transformations