Some invariant solutions of coupled Konno-Oono equations arising in electromagnetic and quantum fields

Abstract

The goal of this study is to construct a novel family of travelling wave solutions for the system of (1 + 1)-coupled Konno-Oono equations (CKOEs). It occurs in optical nonlinear media, electromagnetic fields, plasma physics, and quantum fields. The invariant property of Lie symmetry analysis is exploited to extract analytical solutions. Lie symmetry analysis provides new similarity solutions for the system. A new variety of eighteen analytical solutions are compared to the reported results and the authors’ recently published work. In the previous results, a specific form of CKOEs with only two components, u and v, was solved in almost all cases, whereas in this study, a family of solutions was attained for three variables, u, v, and w. Solution profiles are portrayed via numerical simulation in order to make the solutions physically relevant.

Some more variety of analytical solutions to (2+1)-Bogoyavlensky-Konopelchenko equation

“…There are numerous intricate natural phenomena in our lives and surroundings that have many implications. Such phenomena are often described by nonlinear evolution equations (NLEEs), which occur in fields such as fluid mechanics [1], genetic theories [2], condensed materials science [3], marine science [4], optical and computational physics [5], plasma physics [6,7], chaotic sciences [8] and other fields [9]. The significance of NLEEs attracted the research community due to their distinctive properties.…”

A study on analytical solutions and conservation laws of the cgKP occurring in straits

“…Therefore, the Lie group is used in a variety of contexts, including the construction of explicit solutions to PDEs. The physical significance and theoretical analysis of the proposed method have been investigated in the existing literature [17,18,[39][40][41][42][43][44][45][46].…”

CTE Solvability, Nonlocal Symmetry, and Interaction Solutions of Coupled Integrable Dispersionless System

“…A large number of useful methods have been investigated, such as the inverse scattering transformation [1-3], Hirota's bilinear method [4], symmetry reductions [5][6][7], the Darboux transformation [8], the Painlevé analysis method [9], the Bäcklund transformation (BT) [10], the separated variable method [11], etc [12,13]. e similarity solutions can be found by the Lie point symmetry method [14,15]. To describe the complex physical phenomena, the interactions among different nonlinear excitations are worth studying compared with soliton solutions [16][17][18][19].…”