Breather wave, lump type and interaction solutions for a high dimensional evolution model

This paper studies on an evolution model by means of bilinear neural network method, which is a high dimensional model. Firstly, we give the structure framework and the pattern of the bilinear neural network. Secondly, with choosing appropriate activation functions and neuron coefficients by means of Hirota bilinear form, we get many new meaningful exact solutions, including breather wave, two types interaction phenomena and two multi-layer exact solutions, one of the interaction solutions is obtained by using the new test function which is first attempt by authors, including lump function, biexponential function and cosine function. The interaction of absorption, escape and reabsorption between lump type and two-solitons-like waves occurs at patterns 3-4-1 and 3-5-1. Such an interaction phenomenon has significant impaction on the research of nonlinear fields. At last, the figures of exact solutions are exhibited by selecting suitable neuron coefficients.