In this paper, we discuss the Hamiltonian structure of Korteweg–de Vries equation, modified Korteweg–de Vries equation, and generalized Korteweg– de Vries equation. We proposed the Sine-function algorithm to obtain the exact solution for non-linear partial differential equations. This method is used to obtain the exact solutions for KdV, mKdV and GKdV equations. Also, we have applied the method...

In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.

The fundamental matrix solution of the quantum Knizhnik-Zamolodchikov equation associated with Uq(ŝl2) is constructed for |q| = 1. The formula for its determinant is given in terms of the double sine function.

The fundamental matrix solution of the quantum Knizhnik-Zamolodchikov equation associated with Uq(ŝl2) is constructed for |q| = 1. The formula for its determinant is given in terms of the double sine function.

In this article, we study the numerical solution of the one dimensional nonlinear sineGordon by using the modified cubic B-spline differential quadrature method (MCB-DQM). The scheme is a combination of a modified cubic B-spline basis function and the differential quadrature method. The modified cubic B-spline is used as a basis function in the differential quadrature method to compute the weig...

We prove global well-posedness of the short-pulse equation with small initial data in Sobolev spaceHs for an integer s ≥ 2. Our analysis relies on local well-posedness results of Schäfer & Wayne [12], the correspondence of the short-pulse equation to the sine– Gordon equation in characteristic coordinates, and a number of conserved quantities of the short-pulse equation. We also prove local and...

The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG ...

Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super Bäcklund transformation and is further used to obtain N super soliton solutions. PACS: 02.30.Ik PACS: 12.60.Jv mohsin [email protected] On study leave from PRD (PINSTECH) Islamabad, Pakistan mhassa...

In this paper, based on the generalized Jacobi elliptic function expansion method,we obtain abundant new complex doubly periodic solutions of the double Sine-Gordon equation (DSGE), which are degenerated to solitary wave solutions and triangle function solutions in the limit cases,showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations i...

In this article, we shall prove a result which enables us to transfer from finite infinite Euler products. As an example, give two new proofs of the product for sine function depending on certain decompositions. We then some equivalent expressions functional equation, i.e. partial fraction expansion and integral expression involving generating Bernoulli numbers. The equivalence functions hyperb...