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...

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...

We solve exactly the “boundary sine-Gordon” system of a massless scalar field φ with a cosβφ/2 potential at a boundary. This model has appeared in several contexts, including tunneling between quantum-Hall edge states and in dissipative quantum mechanics. For β < 8π, this system exhibits a boundary renormalization-group flow from Neumann to Dirichlet boundary conditions. By taking the massless ...

We find new periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating solutions of nonlinear differential equations is successful as a consequence of some powerful, recen...

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficents can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counter-terms. We a...

New exact solutions with built-in arbitrary functions for the (n + 1)-dimensional double sine-Gordon equation are studied by means of auxiliary solutions of the cubic nonlinear Klein–Gordon (CNKG) fields. By a proper selection of the arbitrary functions and the appropriate solutions of the CNKG systems, new solutions including periodic-solitoffs, periodic-twisted kinks, quasi-periodic and non-p...

A family of deformed models the sine–Gordon-type can be generated by twisting sine–Gordon model. As a particular case, 3-sine–Gordon model is here addressed, whose differential configurational entropy and complexity three topological sectors are discussed using two complementary approaches. Stability aspects also discussed.