Solitons, periodic waves, breathers and integrability for a nonisospectral and variable-coefficient fifth-order Korteweg-de Vries equation in fluids

Under investigation in this paper is a nonisospectral and variable-coefficient fifth-order Korteweg-de Vries equation in fluids. By virtue of the Bell polynomials and symbolic computation, the bilinear form, Bäcklund transformation and Lax pair are obtained. Based on its bilinear form, N-soliton solutions are constructed. Furthermore, periodic wave and breather wave solutions are obtained by virtue of the Riemann theta function and homoclinic test approach, respectively. In addition, the characteristic-line method is applied to discuss the features of the solitons for the nonisospectral problem, such as the amplitude, velocity and width of the solitary wave.