Nonlinear partial differential equations are of particular interest to mathematicians and physicists because of their ability to model a wide range of complex nonlinear phenomena. Consequently, obtaining their exact analytical solutions is of considerable importance. In this study, we invoked the Lie symmetry method to construct new exact explicit solutions to a generalized 2D B-type Kadomtsev-Petviashvili (2D-gnBKP) equation. The Lie symmetry method provides a systematic framework for identifying continuous symmetries admitted by a differential equation and, subsequently, reducing its order and complexity. First, the infinitesimal generators were derived and using these, a one-dimensional optimal system of subalgebras was constructed. The optimal system enables the classification of inequivalent symmetry reductions and avoids redundant solution representations. Thereafter, symmetry reductions were performed that reduce the 2D-gnBKP equation to multiple ordinary differential equations. These reduced equations were then analyzed using a variety of analytical techniques. In particular, exact solutions were obtained through direct integration, the simplest equation, $ (G'/G) $-expansion, and Kudryashov's techniques. Finally, for the first time in the literature, we constructed conserved vectors for the equation using the multiplier approach and Ibragimov's method. The resulting conserved quantities include physically meaningful conservation laws related to momentum and energy, thereby highlighting important structural and physical properties of the model.
Citation: Chaudry Masood Khalique, Jonathan Lebogang Bodibe. Analytical and dynamical investigation of novel solutions and conserved vectors for a generalized 2D B-type Kadomtsev-Petviashvili equation of fluid dynamics[J]. Electronic Research Archive, 2026, 34(12): 8917-8942. doi: 10.3934/era.2026375
Nonlinear partial differential equations are of particular interest to mathematicians and physicists because of their ability to model a wide range of complex nonlinear phenomena. Consequently, obtaining their exact analytical solutions is of considerable importance. In this study, we invoked the Lie symmetry method to construct new exact explicit solutions to a generalized 2D B-type Kadomtsev-Petviashvili (2D-gnBKP) equation. The Lie symmetry method provides a systematic framework for identifying continuous symmetries admitted by a differential equation and, subsequently, reducing its order and complexity. First, the infinitesimal generators were derived and using these, a one-dimensional optimal system of subalgebras was constructed. The optimal system enables the classification of inequivalent symmetry reductions and avoids redundant solution representations. Thereafter, symmetry reductions were performed that reduce the 2D-gnBKP equation to multiple ordinary differential equations. These reduced equations were then analyzed using a variety of analytical techniques. In particular, exact solutions were obtained through direct integration, the simplest equation, $ (G'/G) $-expansion, and Kudryashov's techniques. Finally, for the first time in the literature, we constructed conserved vectors for the equation using the multiplier approach and Ibragimov's method. The resulting conserved quantities include physically meaningful conservation laws related to momentum and energy, thereby highlighting important structural and physical properties of the model.
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Chaudry Masood Khalique, Jonathan Lebogang Bodibe. Analytical and dynamical investigation of novel solutions and conserved vectors for a generalized 2D B-type Kadomtsev-Petviashvili equation of fluid dynamics[J]. Electronic Research Archive, 2026, 34(12): 8917-8942. doi: 10.3934/era.2026375
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