Bright solitons in coherently coupled nonlinear Schrödinger equations with alternate signs of nonlinearities

Abstract

The exact bright one- and two-soliton solutions of a particular type of coherently coupled nonlinear Schrödinger equations, with alternate signs of nonlinearities among the two components, are obtained using the non-standard Hirota's bilinearization method. We find that in contrary to the coherently coupled nonlinear Schrödinger equations with same signs of nonlinearities the present system supports only coherently coupled solitons arising due to an interplay between dispersion and the nonlinear effects, namely, self-phase modulation, cross-phase modulation, and four-wave mixing process, thereby depend on the phases of the two co-propagating fields. The other type of soliton, namely, incoherently coupled solitons which are insensitive to the phases of the co-propagating fields and arise in a similar kind of coherently coupled nonlinear Schrödinger equations but with same signs of nonlinearities are not at all possible in the present system. The present system can support regular solution for the choice of soliton parameters for which mixed coupled nonlinear Schrödinger equations admit only singular solution. Our analysis on the collision dynamics of the bright solitons reveals the important fact that in contrary to the other types of coupled nonlinear Schrödinger systems the bright solitons of the present system can undergo only elastic collision in spite of their multicomponent nature. We also show that regular two-soliton bound states can exist even for the choice for which the same system admits singular one-soliton solution. Another important effect identified regarding the bound solitons is that the breathing effects of these bound solitons can be controlled by tuning the additional soliton parameters resulting due to the multicomponent nature of the system which do not have any significant effects on bright one soliton propagation and also in soliton collision dynamics.

Nonstandard bilinearization ofPT-invariant nonlocal nonlinear Schrödinger equation: Bright soliton solutions

“…[13]. As we pointed out earlier the velocities of the solitons are determined by the parameters 2k 1R and 2k 2R and the central positions of the solitons are given by the parameters…”

“…[4], the two parameter breathing soliton solution (16) develops singularity in a finite time as may be checked from condition (13) for the choice k 1R =k 1R = 0, k 1I = 2η 1 ,k 1I = 2η 1 , α 1 = −2(η 1 +η 1 )e iθ 1 and…”

Novel energy sharing collisions of multicomponent solitons

“…Additionally, there exists another integrable 2-CCNLS system with nonlinearities having opposite signs in the two components, for which the soliton solutions and bound states are constructed in Ref. [25]. As the solitons in this system undergo standard elastic collision we do not discuss this system in this review.…”

“…A standard bilinearization procedure will result in a greater number of bilinear equations than the number of bilinearising variables, which results in soliton solutions with less number of arbitrary parameters. In order to get more general soliton solutions we introduce an auxiliary function during the bilinearization of the m-CCNLS system which gives equal number of bilinear equations and variables [23][24][25][26][27]. To be more clear with the presentation, we give below the bilinear equations for the m-CCNLS system (5)…”

(2+1)-dimensional local and nonlocal reductions of the negative AKNS system: Soliton solutions

“…The coefficients of ε 3 vanish with the dispersion relations and (6.7). From the coefficient of 8) and this equation also vanishes directly due to the dispersion relations and (6.7). Without loss of generality let us also take ε = 1.…”