Fakir Chand

Series solutions to the N-dimensional radial Schrödinger equation for the quark–antiquark interaction potential

In this work, we analytically obtain the energy eigenvalues and normalized eigenfunctions of the radial Schrodinger equation in N-dimensional Hilbert space for the quark–antiquark interaction potential using the power series technique via a suitable ansatz to the wavefunction. From the energy eigenvalues, the mass spectra of heavy quarkonia in three dimensions are obtained. The problem is also solved numerically. The obtained analytical and numerical results are in good agreement with the existing results.

Exact travelling wave solutions of some nonlinear equations by G′G-expansion method

Abstract Here we find exact solutions of some nonlinear evolution equations within the framework of the G ′ G -expansion method. Exact solutions of five nonlinear equations of physical importance viz. the coupled Schrodinger–KdV equation, the coupled nonlinear Reaction–Diffusion equation, the Foam Drainage equation, the Phi-Four equation and the Dodd–Bullough–Mikhailov equation are obtained. These general solutions can be reduced in some standard results derived by some other methods. Two and three dimensional plots of some of the results are also presented.

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.

Solution of Schrödinger Equation for Two-Dimensional Complex Quartic Potentials

We investigate the quasi-exact solutions of the Schr?dinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out.

The solution of the Schrödinger equation for complex Hamiltonian systems in two dimensions

We investigate the ground state solutions of the Schrodinger equation for complex (non-Hermitian) Hamiltonian systems in two dimensions within the framework of an extended complex phase-space approach. The eigenvalues and eigenfunctions of some two-dimensional complex potentials are found.

Construction of exact dynamical invariants of two-dimensional classical system

A general method is used for the construction of second constant of motion of fourth order in momenta using the complex coordinates (z,z-). A fourth-order potential equation is obtained whose solutions directly provide a large class of integrable systems. The potential equation is tested with an interesting example which admits second constants of motion.

Energy Spectra of the Coulomb Perturbed Potential in N-Dimensional Hilbert Space

We deal with the solutions to the radial Schrodinger equation for the Coulomb perturbed potential in N-dimensional Hilbert space by using two methods, i.e. the power series technique via a suitable ansatz to the wavefunction and the Virial theorem. Analytic expressions for eigenvalues and normalized eigenfunctions are derived. A recursion relation among series expansion coefficients, a condition for convergence of series and inter-dimensional degeneracies are also investigated. As special cases, the problem is solved in 3 and 4 dimensions with some specific parameter values. The obtained analytical and numerical results are in good agreement with the results of other studies.

Reply to Comment on ‘Series solutions to the N-dimensional radial Schrödinger equation for the quark–antiquark interaction potential’

In this reply, we address the issues raised in the comment by Fernandez (2012 Phys. Scr. 86 027001) on our work, Kumar and Chand (2012 Phys. Scr. 85 055008).