Stability of the Bright-Type Algebraic Solitary-Wave Solutions of Two Extended Versions of the Nonlinear Schrödinger Equation

Abstract

The stability of the bright-type algebraic solitary-wave solutions of two extended nonlinear Schrödinger (NLS) equations, recently obtained by Hayata and Koshiba (HK) [Phys. Rev. E 51 (1995) 1499], is investigated by means of the averaged Lagrangian variational technique. Concerning the first equation (a quadratic-cubic NLS eq.), the variational analysis shows that the exact solution found by HK is stable, as solitary-wave initial conditions which deviate from the HK solution evolve into oscillatory functions whose envelopes remain close to the exact solution, if certain stability conditions are satisfied. Concerning the second equation (a cubic-quintic NLS eq.), the variational analysis indicates that in this case the exact solution is unstable, as solitary-wave initial conditions which are higher than the exact solution lead to a blowup within a finite distance, whereas initial pulses which are lower than the exact solution are completely dispersed.