Using Painleve singularity structure analysis, we show that coupled higher-order nonlinear Schrodinger (CHNLS) equations admit the Painleve property. Using the results of the Painleve analysis, we succeed in Hirota bilinearizing the CHNLS equations for the integrable cases. Solving the Hirota bilinear equations, one soliton and two soliton solutions are explicitly obtained. Lax pairs are explic...

Abstact. For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it is true then in case the Painleve equations I and II an explicite change of variables is given that is written using the differential invariants of...

A method for solving certain nonlinear ordinary and partial differential equations is developed. The central idea is to study monodromy preserving deformations of linear ordinary differential equations with regular and irregular singular points. The connections with isospectral deformations and with classical and recent work on monodromy preserving deformations are discussed. Specific new resul...

By using an extended ( ′ G )-expansion method, we construct the traveling wave solutions of the (2+1)dimensional Painleve integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Veselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations, where G satisfies the second order linear ordinary differential equation. By...

The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point t∗ and fast oscillating behavior after the point t∗. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficient...

dynamically adaptive numerical methods have been developed to find solutions for differential equations. thesubject of wavelet has attracted the interest of many researchers, especially, in finding efficient solutions fordifferential equations. wavelets have the ability to show functions at different levels of resolution. in this paper, a numerical method is proposed for solving the second pain...

We announce a generalization of the reduction theorem for 0parameter solutions of the traditional (i.e., second order) Painlevé equations with a large parameter to those of some higher order Painlevé equations, i.e., each member of the Painleve hierarchies (PJ) (J =I, II-1 and II-2) discussed in [KKNT]. Thus the scope of applicability of the reduction theorem ([KT1], [KT2]) has been substantial...

In this paper, a singularity structure analysis of the (2+1)-dimensional Zakharov equation is carried out and it is shown that it admits the Painleve property. The bilinear form of this equation is derived from the Painleve analysis in a straightforward manner. Using this bilinear form, we have constructed the simply one soliton solution by the Hirota method. We have then presented the localize...