The nonlocal potential transformation method and solitary wave solutions for higher dimensions in shallow water waves

Abstract

In this paper, the integrable (4 + 1)-dimensional Fokas equation is investigated. Exploiting a set of non-singular local multipliers, we present a set of local conservation laws for the equation. The nonlocally related partial differential equation (PDE) systems are found. Nine nonlocally related systems are discussed reveal thirty five interesting closed form solutions of the equation. These solutions contain different types of wave solutions, double soliton, multi-solitons, kink and periodic wave solutions. Some of the resulting solutions are graphically illustrated. Furthermore, we apply the sine-cosine method to find other traveling wave solutions for this equation.

KEYWORDS:

• Lie point symmetry
• conservation law
• soliton solutions
• (4 + 1)-dimensional nonlinear Fokas equation
• nonlocal potential similarity transformation

Disclosure statement

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