1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity
Abstract This paper obtains the 1-soliton solution of the Jaulent–Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence.
Solitary wave and shock wave solitons to the transmission line model for nano-ionic currents along microtubules
In this letter, the solitary wave and shock wave solitons for nonlinear equation of special interest in nanobiosciences, namely the transmission line model for nano-ionic currents along microtubules, have been constructed successfully. The solitary wave ansatz is used to carry out the solutions which shows the consistency.
Application of the Adomian decomposition method for the Fokker-Planck equation
In this work we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the Fokker-Planck equation and some similar equations. This method can successfully be applied to a large class of problems. The Adomian decomposition method needs less work in comparison with the traditional methods. This method decreases considerable volume of calculations. The decomposition procedure of Adomian will be obtained easily without linearizing the problem by implementing the decomposition method rather than the standard methods for the exact solutions. In this approach the solution is found in the form of a convergent series with easily computed components. In this work we are concerned with the application of the decomposition method for the linear and nonlinear Fokker-Planck equation. To give overview of methodology, we have presented several examples in one and two dimensional cases.