Solitary waves of the generalized Radhakrishnan-Kundu-Lakshmanan equation with four powers of nonlinearity

The complex Radhakrishnan-Kundu-Lakshmanan equation having polynomial law of nonlinearity with four powers is considered. The Cauchy problem for this partial differential equation cannot be solved by the inverse scattering transform and the exact solutions of this equation is looked for taking into account the traveling wave variables. The overdetermined system of nonlinear ordinary differential equations for the real and imaginary parts of the ordinary differential equation obtained is presented. The compatibility conditions are obtained. First integral of the nonlinear differential equation is found. It is shown that there exist periodic solutions of the mathematical model. Solitary wave solutions of the complex Radhakrishnan-Kundu-Lakshmanan equation are given in the form of implicit functions using the direct and special methods. (c) 2022 Elsevier B.V. All rights reserved.