arXiv subjects

Benoy Talukdar

Publications and source records attributed to Benoy Talukdar.

21 records · Page 2Linked to original sources

arXiv2013

Factorization method for nonlinear evolution equations Factorization method for nonlinear evolution equations

The traditional method of factorization can be used to obtain only the particular solutions of the Liénard type ordinary differential equations. We suggest a modification of the approach that can be used to construct general solutions . We first demonstrate the effectiveness of our method by dealing with a solvable form of the modified Emden-type equation and subsequently employ it to obtain the solitary wave solutions of the KdV, mKdV, Rosenau-Hyman (RH) and NLS equations. The solution of the mKdV equation, via the so-called Muira transform, leads to a singular solution of the KdV equation in addition to the well-known soliton solution supported by it. We obtain the solution of the non-integrable RH equation in terms of the Jacobi function and show that, although robust, it is structurally different from the KdV soliton. We also find the soliton solution of the NLS equation that accounts for the evolution of complex envelopes in an optical medium.

nlin.SI↗

arXiv2013

On the non-standard Lagrangian equations

In an attempt to look for the root of nonstandard Lagrangians in the theories of the inverse variational problem we introduce a logarithmic Lagrangian (LL) in addition to the so-called reciprocal Lagrangian (RL) that exists in the literature. The equation of motion that follows from the RL could easily be solved by using its first or Jacobi integral. This is not, however, true for the similar equation resulting from the LL. We make use of a method of factorization to find the particular solutions for equations following from both RL an LL and subsequently derive a novel approach to obtain their general solutions from the particular ones. The case studies presented by us include the modified Emden-type equation for which we also construct a new expression for the Lagrangian function (NL). We point out that NL is not related to RL by a total derivative or gauge term. In spite of that NL leads to the same equation of motion as that given by the RL.

nlin.SI↗

arXiv2012

Displaced dynamics of binary mixtures in linear and nonlinear optical lattices

The dynamical behavior of matter wave solitons of two-component Bose-Einstein condensates (BEC) in combined linear and nonlinear optical lattices (OLs) is investigated. In particular, the dependence of the frequency of the oscillating dynamics resulting from initially slightly displaced components is investigated both analytically, by means of a variational effective potential approach for the reduced collective coordinate dynamics of the soliton, and numerically, by direct integrations of the mean field equations of the BEC mixture. We show that for small initial displacements binary solitons can be viewed as point masses connected by elastic springs of strengths related to the amplitude of the OL and to the intra and inter-species interactions. Analytical expressions of symmetric and anti-symmetric mode frequencies, are derived and occurrence of beatings phenomena in the displaced dynamics is predicted. These expressions are shown to give a very good estimation of the oscillation frequencies for different values of the intra-species interatomic scattering length, as confirmed by direct numerical integrations of the mean field Gross-Pitaevskii equations (GPE) of the mixture. The possibility to use displaced dynamics for indirect measurements of BEC mixture characteristics such as number of atoms and interatomic interactions is also suggested.

cond-mat.quant-gas↗