STABILITY OF THE BRIGHT-TYPE ALGEBRAIC SOLITARY-WAVE SOLUTIONS OF 2 EXTENDED VERSIONS OF THE NONLINEAR SCHRODINGER-EQUATION

The stability of the bright-type algebraic solitary-wave solutions of two extended nonlinear Schrodinger (NLS) equations, recently obtained by Hayata and Koshiba (HK) [Phys. Rev. E 51 (1995) 1499], is investiga ted by means of the averaged Lagrangian variational technique. Concern ing the first equation (a quadratic-cubic NLS eq.), the variational an alysis shows that the exact solution found by HK is stable, as solitar y-wave initial conditions which deviate hom the HK solution evolve int o oscillatory functions whose envelopes remain close to the exact solu tion, if certain stability conditions are satisfied. Concerning the se cond equation (a cubic-quintic NLS eq.), the variational analysis indi cates that in this case the exact solution is unstable, as solitary-wa ve initial conditions which are higher than the exact solution lead to a blowup within a finite distance, whereas initial pulses which are l ower than the exact solution are completely dispersed.