Discrete N-fold Darboux transformation and infinite number of conservation laws of a four-component Toda lattice

In this paper, we investigate a four-component Toda lattice (TL), which may be used to model the wave propagation in lattices just like the famous TL. By means of the Lax pair and gauge transformation, we construct the [Formula: see text]-fold Darboux transformation (DT), which enables us to obtain multi-soliton or multi-solitary wave solution without complex iterative process. Through the obtained DT, [Formula: see text]-fold explicit exact solutions of the system and their figures with proper parameters are presented from which we find the [Formula: see text]-fold solution shows two-solitary wave structure, the amplitude and shape of the wave change with time. Finally, we derive an infinite number of conservation laws formulaically to illustrate the integrability of the system.

Solitary wave solution of nonlinear Bogoyavlenskii system by variational analysis method

In this work, the Bogoyavlenskii system (BS) and fractal BS are investigated by variational method for the first time. An efficient and simple scheme is proposed to seek their exact solitary wave solutions, which is called variational analysis method. The novel scheme requires only two steps, making it much attractive in practical applications, and a good result is obtained. This paper cleans up the road to the exact solitions, and it sheds a new light on the soliton theory. Finally, the physical properties of solitary wave solutions obtained are analyzed by some simulation figures.

Exact solutions of the (3+1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation

In this paper, we study exact solutions of the (3[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation. We employ the Hirota bilinear method to obtain the multi-solitary wave solutions, soliton resonant solutions, periodic solutions and interactional solutions and periodic resonant solutions. The corresponding asymptotic features and images are also clearly given.

Solitary Wave Solutions for Some Fractional Evolution Equations via New Kudryashov Approach

In this work, we construct solitary wave solutions of a nonlinear evolution equation in the physical phenomena of waves;namely the time-fractional fifth-order Sawada-Kotera equation and the (4+1)-dimensional space-time fractional Fokas equation by Kudryashov method with a new function. As a result, new types of exact analytical solutions are obtained. Here the fractional derivative is described in beta sense.