Dynamical behavior of similarity solutions of CKOEs with conservation law

Abstract

The propagation of a current-fed string in 3-dimensional space interacting with an external magnetic field is described by the system of coupled Konno–Oono equations. Present research deals with the formation of one, two, and three dimensional optimal sub-algebras of the system. Then invariants are decided by using the Killing form. Similarity reductions and their solutions are determined for each sub-algebra. For strong integrability of the system, conserved vectors are also attained by using Noether’s theorem. The novelty of analytical solutions can be demonstrated by the fact that in earlier studies, all researchers solved coupled Konno–Oono equations involving only two components of the water wave, but in this study, the authors solved its more general form. Some comments are also made to demonstrate that the results in this article are preferable to those in previous studies. To make the solutions physically meaningful, they are reinforced with numerical simulation. Periodic, single soliton, doubly bright, bright and dark multisolitons, asymptotic, travelling waves with dark soliton, progressive, highly progressive, and stationary solutions can be seen in the profiles. Such solutions can be beneficial in optical nonlinearity, electro-magnetics, and quantum fields.