Hyperbolic Nonlinear Schrodinger Equation Research Articles

Analytical optical pulses and bifurcation analysis for the traveling optical pulses of the hyperbolic nonlinear Schrödinger equation

Analytical forms of optical pulses for the hyperbolic nonlinear Schrodinger equation are studied by the extended tanh expansion method and another new method successfully. Some graphical presentations of these analytical optical pulses are presented. Bifurcation analysis of the optical pulses of the hyperbolic nonlinear Schrodinger equation is also presented. All possible phase plots are depicted based on physical parameters. The hyperbolic nonlinear Schrodinger equation supports solitary, periodic, kink, anti-kink and most important superperiodic optical pulses. This study is applicable to understand the features of nonlinear pulses in optical fiber.

Modulation instability analysis, optical solitons and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schrodinger's equation

The current study utilizes the extended sinh-Gordon equation expansion and ($frac{G^{prime}}{G^2}$)-expansion function methods in constructing various optical soliton and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schr${ddot o}$dinger's equation which describes the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics. We secure different kinds of solutions like optical dark, bright, singular, combo solitons as well as hyperbolic and trigonometric functions solutions. Moreover, singular periodic wave solutions are recovered and the constraint conditions which provide the guarantee to the soliton solutions are also reported. In order to shed more light on these novel solutions, graphical features 3D, 2D and contour with some suitable choice of parameter values have been depicted. We also discuss the stability analysis of the studied nonlinear model with aid of modulation instability analysis.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrodinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.

Ultrafast transverse undulation of self-trapped laser beams

The propagation of a self-trapped laser beam in a planar waveguide that exhibits a Kerr nonlinearity and a normal chromatic dispersion is considered. We demonstrate experimentally for the first time to our knowledge that such a beam undergoes an undulation responsible for ultrafast transverse oscillations of its axis. This phenomenon, called ???snake instability???, was predicted theoretically in 1973 by Zakharov and Rubenchik on the basis of a study of the soliton solutions of the hyperbolic nonlinear Schr odinger equation. The signature of this instability is observed in the spatially resolved temporal spectrum.