The analysis of differential equations using Lie symmetry has been proved a very robust tool. It is also powerful technique for reducing the order and nonlinearity equations. equation allows dynamic framework establishment invariant solutions initial value boundary problems, deduction laws conservations. This article aimed at applying to fractional-order coupled nonlinear complex Hirota system ...

Collocation method using quintic B-splines finite element have been developed for solving numerically the HirotaSatsuma coupled MKdV equation. Accuracy of the proposed method is shown numerically by calculating conservation laws, 2 L and  L norms on studying of a soliton solution. It is shown that the collocation scheme for solutions of the MKdV equation gives rise to smaller errors and is qui...

The Hirota–Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota–Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge tran...

Abstract: In this paper, we studied the numerical solution of a time-fractional Korteweg–de Vries (KdV) equation with new generalized fractional derivative proposed recently. The fractional derivative employed in this paper was defined in Caputo sense and contained a scale function and a weight function. A finite difference/collocation scheme based on Jacobi–Gauss–Lobatto (JGL) nodes was applie...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV equation. The solution for multiple collisions of super-solitons is given.