Searcharxiv⌕ Search

arXiv subjects

Asish Ganguly

Publications and source records attributed to Asish Ganguly.

9 recordsLinked to original sources
arXiv2012

New Multi-order exact solutions for a class of nonlinear evolution equations

We seek multi-order exact solutions of a generalized shallow water wave equation along with those corresponding to a class of nonlinear systems described by the KdV, modified KdV, Boussinesq, Klein-Gordon and modified Benjamin-Bona-Mahony equation. We employ a modified version of a generalized Lame equation and subject it to a perturbative treatment identifying the solutions order by order in terms of Jacobi elliptic functions. Our multi-order exact solutions are new and hold the key feature that they are expressible in terms of an auxiliary function f in a generic way. For appropriate choices of f we recover the previous results reported in the literature.

nlin.SI↗
arXiv2010

New Exact Solutions of a Generalized Shallow Water Wave Equation

In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic elliptic integral function and doubly-periodic Jacobian elliptic functions. The derived new solutions include rational, periodic, singular and solitary wave solutions. An interesting comparison with the canonical procedure is provided. In some cases the obtained elliptic solution has singularity at certain region in the whole space. For such solutions we have computed the effective region where the obtained solution is free from such a singularity.

nlin.SI↗
arXiv2008

Supersymmetric partners for the associated Lame potentials

The general solution of the stationary Schrodinger equation for the associated Lame potentials with an arbitrary real energy is found. The supersymmetric partners are generated by employing seeds solutions for factorization energies inside the gaps.

math-ph↗
arXiv2006

Exactly solvable associated Lame potentials and supersymmetric transformations

A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are used to generate new exactly solvable potentials; some of them exhibit an interesting property of periodicity defects.

quant-ph↗
arXiv2005

New supersymmetric partners for the associated Lame potentials

We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The formalism of supersymmetric quantum mechanics is used to generate new exactly solvable potentials.

quant-ph↗
arXiv2002

New classes of quasi-solvable potentials, their exactly-solvable limit and related orthogonal polynomials

We have generated, using an sl(2,R) formalism, several new classes of quasi-solvable elliptic potentials, which in the appropriate limit go over to the exactly solvable forms. We have obtained exact solutions of the corresponding spectral problems for some real values of the potential parameters. We have also given explicit expressions of the families of associated orthogonal polynomials in the energy variable.

math-ph↗
arXiv2002

Associated LamÉ Equation, Periodic Potentials and sl(2,R)

We propose a new approach based on the algebraization of the Associated Lamé equation \[-ψ''(x) + [ m(m+1)k^{2}sn^{2}x + \ell(\ell+1)k^{2}(cn^{2}x/dn^{2}x)]ψ(x) = Eψ(x)\] within sl(2,R) to derive the corresponding periodic potentials. The band edge eigenfunctions and energy spectra are explicitly obtained for integers m,$\ell$. We also obtain the explicit expressions of the solutions for half-integer m and integer or half-integer $\ell$.

math-ph↗