We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation zyy + (1/z)xx + 2 = 0. The transformation is related to the special case of the famous Bäcklund transformation of the sine-Gordon equation with the Bäcklund parameter λ = ±1. It is also a nonlocal symmetry.

We prove that the Schäfer–Wayne short pulse equation (SPE) which describes the propagation of ultra-short optical pulses in nonlinear media is integrable. First, we discover a Lax pair of the SPE which turns out to be of the Wadati–Konno–Ichikawa type. Second, we construct a chain of transformations which relates the SPE with the sine-Gordon equation.

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...

The solitons and kinks of the generalized sl(3,C) sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the tau functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions and the soliton masses formulae. As a reduced submodel we obtain the double sine-G...

We introduce a new type of splitting method for semilinear partial differential equations. The method is analyzed in detail for the case of the two-dimensional static sine-Gordon equation describing a large area Josephson junction with overlap current feed and external magnetic field. The solution is separated into an explicit term that satisfies the one-dimensional sine-Gordon equation in the ...

Spatiotemporal chaos arising from the competition between sine-Gordonbreather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov’s method is applied to the resulting effective equation of motion to estimate the parameterspace regions of the ac force where homoclinic bifurcations are induced. The analysis reveals t...