The Generalized Version of Dressing Method with Applications to AKNS Equations

Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients

In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...

the modified exp-function method and its applications to the generalized k(n,n) and bbm equations with variable coefficients

in this article, the modified exp-function method is used to construct many exact solutions to the nonlineargeneralized k(n,n) and bbm equations with variable coefficients. under different parameter conditions, explicitformulas for some new exact solutions are successfully obtained. the proposed solutions are found to beimportant for the explanation of some practical physical problems.

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

Generalized dressing method for nonlinear evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media.

A generalized dressing method is presented for integration of the nonlinear evolution equation of the coherent density function describing partially coherent wave propagation in a noninstantaneous Kerr media. As an example an exact, partially coherent multisource N-soliton solution is derived. It is also demonstrated how this method is applicable for construction of solutions to the equivalent ...