Narrow Results

In this paper, the nonlinear $(1+n)$-dimensional generalized Camassa–Holm Kadomtsev–Petviashvili (g-CH-KP) equation is examined using Lie theory. Lie point symmetries of the equation are computed using MAPLE software and are generalized for the case of any dimension. Moreover, the equation is transformed into a nonlinear ordinary differential equation using the Abelian subalgebra. The nonlinear self-adjoint classification of the equation under consideration is accomplished with the help of which conservation laws for a particular dimension are calculated. Moreover, the new extended algebraic approach is used to compute a wide range of solitonic structures using different set of parameters. Graphic description of some specific applicable solutions for certain physical parameters is portrayed.

The $(G^{\prime }/G)$-expansion scheme is used to execute many wave results for the partial differential equation, namely, the nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation which plays a significant role in mathematical physics, and this equation is accomplished in quantum electron–positron–ion magneto plasmas. The Lie approach is used to find the infinitesimal generators, and group invariant solutions, and help us to reduce the considered PDEs into ODEs. Then a planer dynamical system approach is used to see the existence of closed-form solutions. All possible phase portraits are obtained and the existence of electrostatic wave potentials is reported. Meantime, periodic and super-nonlinear electrostatic wave potentials are found for different initial value conditions with the help of the Runge–Kutta method. Moreover, new traveling wave patterns of the considered models are constructed and presented graphically. Then, the conserved vectors of the given physical model with the use of the multiplier scheme are presented.