Abstract:In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the first time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the first time, we construct the conservation laws of the underlying equation using the multiplier method.

This paper aims to study the extended generalized (2+1)-dimensional Jaulent–Miodek equation (egJM), which arises in a number of significant nonlinear problems of physics and applied mathematics. We derive conservation laws using Noether theorem and find travelling wave solution of the egJM equation.

The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

In this paper we study a nonlinear multi-dimensional partial differential equation, namely, a generalized second extended (3+1)-dimensional Jimbo-Miwa equation. We perform symmetry reductions of this equation until it reduces to a nonlinear fourth-order ordinary differential equation. The general solution of this ordinary differential equation is obtained in terms of the Weierstrass zeta function. Also travelling wave solutions are derived using the simplest equation method. Finally, the conservation laws of the underlying equation are computed by employing the conservation theorem due to Ibragimov, which include conservation of energy and conservation of momentum laws.

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