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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. [ABSTRACT FROM AUTHOR]

In this paper, the symmetry analysis and conservation laws of time fractional coupled Ablowitz–Kaup–Newell–Segur (AKNS) equations have been presented. Initially, the Lie symmetry method has been used for similarity reduction of time fractional coupled AKNS equations. Here, the Erdélyi–Kober differential operators have been used for symmetry reduction. Also, the new conservation vectors for time fractional coupled AKNS equations have been derived by using the new conservation theorem with formal Lagrangian. [ABSTRACT FROM AUTHOR]

This paper introduces a systematic approach to investigate a higher order nonlinear dispersive wave equation for modeling different wave modes. We present both the conventional KdV-type soliton and anomaly type solitons for the equation. We also show the conservation laws and Hamiltonian structures for the equation. Our results suggest that the underlying equation has more interacting soliton phenomena than one would have known for the classical KdV and Boussinesq equation. [ABSTRACT FROM PUBLISHER]