Abstract The spectral characteristics viz. reflectivity, bandwidth, and sidelobes’ intensity for uniform apodized (Gaussian, hyperbolic tangent, apod1, sine, raised sine) fiber Bragg gratings (FBGs) were studied as a function of grating length index modulation. optimal modulation to obtain maximum reflectivity minimum sidelobes determined, needed sensing applications. impact various apodization...

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...

We classify from Lie symmetry standpoint the hyperbolic heat equation with temperature-dependent medium properties. We prove that the hyperbolic heat equation may admit a two-, three-, fouror infinitedimensional symmetry Lie algebra depending on the functional form of density, thermal conductivity, and specific heat. The last possibility corresponds to exactly linearizable hyperbolic heat equat...

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...

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeomet-ric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E 7 (ellip-tic, hyperbolic) and of type E 6...

We propose a new modeling strategy to build efficient neural network representations of chemical kinetics. Instead fitting the logarithm rates, we embed hyperbolic sine function into neural...

In this research work, we successfully construct various kinds of exact traveling wave solutions such as trigonometric like, singular and periodic well hyperbolic to the (2+1)-dimensional Chiral nonlinear Schröginger equation (CNLSE) which is used a governing discuss in quantum field theory. The mechanisms are obtain these extended rational sine-cosine/sinh-cosh constraint conditions for existe...

We derive a new algorithm for computing the action f(A)V of the cosine, sine, hyperbolic cosine, and hyperbolic sine of a matrix A on a matrix V , without first computing f(A). The algorithm can compute cos(A)V and sin(A)V simultaneously, and likewise for cosh(A)V and sinh(A)V , and it uses only real arithmetic when A is real. The algorithm exploits an existing algorithm expmv of Al-Mohy and Hi...

We prove the existence of strong solutions to a class of inhomogeneous boundary-value problems for an elliptic-hyperbolic equation. The equation is an arbitrarily small lower-order perturbation of an equation that arises in the linearization of an approximate model for high-frequency waves near a caustic. The domain boundary is allowed to extend into both the elliptic and hyperbolic regions of ...

The Sine-Gordon equation in (1+3) dimensions has N-traveling front ("kink", "domain wall")- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod system...