A METHOD FOR AN APPROXIMATE SOLUTION TO A PARABOLIC EQUATION WITH A POWER-LAW NONLINEARITY

On convergence of homotopy analysis method to solve the Schrodinger equation with a power law nonlinearity

In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region ...

on convergence of homotopy analysis method to solve the schrodinger equation with a power law nonlinearity

in this paper, the homotopy analysis method (ham) is considered to obtain the solution of the schrodinger equation with a power law nonlinearity. for this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region...

A series solution of the Cauchy problem for the generalized d-dimensional Schrödinger equation with a power-law nonlinearity

Instability of a Parabolic Equation with a Quadratic Nonlinearity

A nonlinear parabolic differential equation with a quadratic nonlinearity is presented which has at least one equilibrium. The linearization about this equilibrium is asymptotically stable, but by using a technique inspired by H. Fujita, we show that the equilibrium is unstable in the nonlinear setting. The perturbations used have the property that they are small in every L p norm, yet they res...

1-Soliton Solution of the Biswas-Milovic Equation With Log Law Nonlinearity

This paper studies the Biswas-Milovic equation with log law nonlinearity. TheGausson solution is obtained by the ansatz method. Subsequently, theconservation laws are derived and the conserved quantities are computed usingthe Gausson solution.