Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations

In this paper, the reverse space cmKdV equation, the reverse time cmKdV equation and the reverse space-time cmKdV equation are constructed and each of three types diverse soliton solutions is derived based on the Hirota bilinear method. The Lax integrability of three types of nonlocal equations is studied from local equation by using variable transformations. Based on exact solution formulae of one- and two-soliton solutions of three types of nonlocal cmKdV equation, some figures are used to describe the soliton solutions. According to the dynamical behaviors, it can be found that these solutions possess novel properties which are different from the ones of classical cmKdV equation.