A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable x and the temporal variable t, and they are exponentially asymptotic to integer multiples of 2π as x → ±∞. The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method p...

For the first time, we study Fokas–Lenells equation in polarization preserving fibers with multiplicative white noise Itô sense. Four integration algorithms are applied, namely, method of modified simple (MMSE), sine-cosine (MSC), Jacobi elliptic (MJEE) and ansatze involving hyperbolic functions. Jacobi-elliptic function solutions, bright, dark, singular, combo dark-bright bright-dark solitons ...

Two sets of super Riccati equations are presented which result in two linear problems of super sine-Gordon equation. The linear problems are then shown to be related to each other by a super gauge transformation and to the super Bäcklund transformation of the equation. PACS: 02.30.Ik PACS: 12.60.Jv On leave of absence from PRD, PINSTECH, Nilore Islamabad (Pakistan).

Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

The term ‘optimization’ refers to the process of maximizing beneficial attributes a mathematical function or system while minimizing unfavorable ones. majority real-world situations can be modelled as an optimization problem. complex nature models restricts traditional techniques obtain global optimal solution and paves path for methods. Particle Swarm Optimization is potential technique that h...