Non classical interaction aspects to a nonlinear physical model

Abstract

This study deals the dynamics of waves to the conformable fractional (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equations. The (2+1)-dimensional NNV equations are the isotropic Lax integrable extension of the (1+1)-dimensional Korteweg–de Vries equations. Fractional differential models (FDMs) from the corresponding integer order model can describes more complex behavior and even cover all properties of integer order model. By the usage of different test approaches, the Hirota bilinear method (HBM) has been successfully applied. The Hirota method is a well-known and reliable mathematical tool for finding the soliton solutions of fractional nonlinear partial differential equations in many fields. However, it demands bilinearization of nonlinear fractional PDE. A class of results in the shapes of lump-periodic, breather-type and two wave solutions have been extracted. Numerical visualizations of the results are also used to demonstrate the implications of the fractionality and parameters. It is acceptable to assume that many experts in engineering models will learn from this research. The results prove the used algorithm is effective, quick, easy, and flexible in its application to various systems.