This investigation offers an innovative analytical strategy, namely the Riccati modified extended simple equation method (RMESEM), to establish and analyze soliton results of the (2+1)-dimensional dynamical generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation (GZK-BBME) in plasma physics. This equation models the physical phenomena of long waves with small and finite amplitude in magnetic plasma. Using a wave transformation, the employed transformative technique first converts GZK-BBME to a nonlinear ordinary differential equation (NODE). With the incorporation of the Riccati equation, a close-form solution is then assumed for the resultant NODE by RMESEM, which converts the NODE into a set of algebraic equations. The fresh plethora of soliton results in the form of rational, exponential, rational-hyperbolic and periodic functional cases are obtained by addressing this set of equations. Several contour, 3D, and 2D graphs are also employed to visualizes the dynamics of these constructed soliton results. These graphs demonstrate that the acquired solitons adopts the type of diverse kink solitons, including cuspon, dark, bright, lump-type, and dark-bright kinks. In addition, our proposed RMESEM shows the applications of the model by producing different traveling soliton results, providing qualitative information on the GZK-BBMEs and possible applications in dealing with other similar kinds of non-linear models.
Citation: Naher Mohammed A. Alsafri, Hamad Zogan. Probing the diversity of kink solitons in nonlinear generalised Zakharov-Kuznetsov-Benjamin-Bona-Mahony dynamical model[J]. AIMS Mathematics, 2024, 9(12): 34886-34905. doi: 10.3934/math.20241661
This investigation offers an innovative analytical strategy, namely the Riccati modified extended simple equation method (RMESEM), to establish and analyze soliton results of the (2+1)-dimensional dynamical generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation (GZK-BBME) in plasma physics. This equation models the physical phenomena of long waves with small and finite amplitude in magnetic plasma. Using a wave transformation, the employed transformative technique first converts GZK-BBME to a nonlinear ordinary differential equation (NODE). With the incorporation of the Riccati equation, a close-form solution is then assumed for the resultant NODE by RMESEM, which converts the NODE into a set of algebraic equations. The fresh plethora of soliton results in the form of rational, exponential, rational-hyperbolic and periodic functional cases are obtained by addressing this set of equations. Several contour, 3D, and 2D graphs are also employed to visualizes the dynamics of these constructed soliton results. These graphs demonstrate that the acquired solitons adopts the type of diverse kink solitons, including cuspon, dark, bright, lump-type, and dark-bright kinks. In addition, our proposed RMESEM shows the applications of the model by producing different traveling soliton results, providing qualitative information on the GZK-BBMEs and possible applications in dealing with other similar kinds of non-linear models.
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Naher Mohammed A. Alsafri, Hamad Zogan. Probing the diversity of kink solitons in nonlinear generalised Zakharov-Kuznetsov-Benjamin-Bona-Mahony dynamical model[J]. AIMS Mathematics, 2024, 9(12): 34886-34905. doi: 10.3934/math.20241661
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