Hitender Kumar

Analytical spatiotemporal soliton solutions to (3+1)-dimensional cubic-quintic nonlinear Schrödinger equation with distributed coefficients

We obtain exact spatiotemporal periodic traveling wave solutions to the generalized (3+1)-dimensional cubic-quintic nonlinear Schrodinger equation with spatial distributed coefficients. For restrictive parameters, these periodic wave solutions acquire the form of localized spatial solitons. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and gain (or loss). We then demonstrate the nonlinear tunneling effects and controllable compression technique of three-dimensional bright and dark solitons when they pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity parameters. Direct numerical simulation has been performed to show the stable propagation of bright soliton with 5% white noise perturbation.

Applications of extended F-expansion and projective Ricatti equation methods to (2+1)-dimensional soliton equations

The (2+1)-dimensional Maccari and nonlinear Schrodinger equations are reduced to a nonlinear ordinary differential equation (ODE) by using a simple transformation, various solutions of the nonlinear ODE are obtained by using extended F-expansion and projective Ricatti equation methods. With the aid of solutions of the nonlinear ODE more explicit traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions are found out. It is shown that these methods provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

DARK AND BRIGHT SOLITARY WAVE SOLUTIONS OF THE HIGHER ORDER NONLINEAR SCHR¨ ODINGER EQUATION WITH SELF-STEEPENING AND SELF-FREQUENCY SHIFT EFFECTS

In this paper, we obtain the exact bright and dark soliton solutions for the nonlin- ear Schrodinger equation (NLSE) which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method is used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses are determined. Using the one-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa-Satsuma cases and finally, we have constructed some periodic wave solutions by reducing the higher order nonlinear Schrodinger equation (HNLS) to quartic anhar- monic oscillator equation. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a HNLS model equation.