The nonlocal potential transformation method for solitary wave packets of a shock-breaking dynamics system

Abstract

In this work, we employ the potential similarity transformation method to derive some solitary wave packet solutions for the Calogero-Bogoyavlenskii-Schiff (CBS) equation. Exploiting nonsingular local multipliers, a set of local conservation laws is presented for the equation. The nonlocally related partial differential equation (PDE) systems were observed. Considering the nonlocal-related PDE systems, we present 46 analytic solutions of the CBS equation that involves several arbitrary functions, enabling the spread of the equation’s solution to understand Riemann waves dynamics extensively. These are helpful in severalapplications such as electromagnetic waves in an optical tsunami in fibers, magneto-sonic and ion in plasma, the acoustic waves in compressible fluids, surface, and interval waves in oceans, tidal and tsunami in rivers.

KEYWORDS:

• Solitary wave packets
• nonlocal potential similarity transformation
• lie point symmetry
• conservation law
• (2 + 1) CBS equation

Disclosure statement

No potential conflict of interest was reported by the author(s).