Avinash Khare | Savitribai Phule Pune University (original) (raw)

Papers by Avinash Khare

Physics Letters A, 1995

We describe three different methods for generating quasi-exactly solvable potentials, for which a... more We describe three different methods for generating quasi-exactly solvable potentials, for which a finite number of eigenstates are analytically known. The three methods are respectively based on (i) a polynomial ansatz for wave functions; (ii) point canonical transformations; (iii) supersymmetric quantum mechanics. The methods are rather general and give considerably richer results than those available in the current literature.

Physical Review E, 2003

We obtain an exact solution for the breather lattice solution of the modified Korteweg de Vries e... more We obtain an exact solution for the breather lattice solution of the modified Korteweg de Vries equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-breather interaction. However, such multibreather structures can be stabilized through the concurrent application of ac driving and viscous damping terms.

Physics Letters A, 2000

We show that the quasi-exactly solvable eigenvalues of the Schrödinger equation for the PT-invari... more We show that the quasi-exactly solvable eigenvalues of the Schrödinger equation for the PT-invariant potential V(x)=−(ζcosh2x−iM)2 are complex conjugate pairs in case the parameter M is an even integer while they are real in case M is an odd integer. We also show that whereas the PT symmetry is spontaneously broken in the former case, it is unbroken in the

Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytic... more Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lamé potentials ma(a+1)sn2(x,m) are computed for integer values a=1,2,3,... . For all cases (except a=1), we show that the partner potential is distinctly different from the original Lamé potential, even

Physics Letters A, 1996

Exact stationary soliton solutions of the fifth order KdV type equation, ut + αupux + βu3x + γu5x... more Exact stationary soliton solutions of the fifth order KdV type equation, ut + αupux + βu3x + γu5x = 0, are obtained for any p (> 0) in case αβ > 0, Dβ > 0, βγ < 0 (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case

Journal of Physics A-mathematical and General, 1993

Quantum mechanical potentials satisfying the property of shape invariance are well known to be al... more Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the

We state and discuss numerous new mathematical identities involving Jacobi elliptic functions sn(... more We state and discuss numerous new mathematical identities involving Jacobi elliptic functions sn(x,m), cn(x,m), and dn(x,m), where m is the elliptic modulus parameter. In all identities, the arguments of the Jacobi functions are separated by either 2K(m)/p or 4K(m)/p, where p is an integer and K(m) is the complete elliptic integral of the first kind. Each p-point identity of rank

Journal of Physics A-mathematical and General, 1996

We give a systematic classification and a detailed discussion of the structure, motion and scatte... more We give a systematic classification and a detailed discussion of the structure, motion and scattering of the recently discovered negaton and positon solutions of the Korteweg - de Vries hierarchy. There are two distinct types of negaton solutions which we label 0305-4470/29/8/027/img6 and 0305-4470/29/8/027/img7, where (n + 1) is the order of the Wronskian used in the derivation. For negatons,

American Journal of Physics, 1988

It is well known that the harmonic oscillator potential can be solved by using raising and loweri... more It is well known that the harmonic oscillator potential can be solved by using raising and lowering operators. This operator method can be generalized with the help of supersymmetry and the concept of ``shape-invariant'' potentials. This generalization allows one to calculate the energy eigenvalues and eigenfunctions of essentially all known exactly solvable potentials in a simple and elegant manner.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

We obtain exact solutions for kinks in ϕ(8), ϕ(10), and ϕ(12) field theories with degenerate mini... more We obtain exact solutions for kinks in ϕ(8), ϕ(10), and ϕ(12) field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order ϕ(4) and ϕ(6) theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the coexistence of up to three distinct kinks (for a ϕ(12) potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have s...

Physical review. E, Statistical, nonlinear, and soft matter physics, 2006

A class of discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities is... more A class of discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrödinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.

Physical review letters, Jan 17, 2002

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lamb... more Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions.

ABSTRACT We give a construction of coherent states for strictly isospectral Hamiltonians by explo... more ABSTRACT We give a construction of coherent states for strictly isospectral Hamiltonians by exploiting the fact that these are related by a unitary transformation, and hence the corresponding coherent states must be related by the same unitary transformation. We give the explicit structure of such a unitary transformation in terms of the eigenvalues and eigenfunctions of a given factorizable Hamiltonian. As an illustration, we discuss the example of strictly isospectral one-dimensional harmonic oscillator Hamiltonians and the associated coherent states, and point out inadequacies in recent constructions of such coherent states in the literature.

Pramana-journal of Physics, 1980

Exact solutions for the motion of a classical anharmonic oscillator in the potentialV(φ)=Bφ 2 − |... more Exact solutions for the motion of a classical anharmonic oscillator in the potentialV(φ)=Bφ 2 − |A|φ 4 +Cφ 6 are obtained in (1 + 1) dimensions. Instanton-like solutions in (imaginary time) which takes the particle from one maximum of the potential to the other are obtained in addition to the usual oscillatory solutions. The energy dependence of the frequencies of