Singular Soliton Molecules of the Nonlinear Schrodinger Equation

Abstract

We derive an exact solution to the local nonlinear Schrödinger equation (NLSE) using the Darboux transformation method. The new solution describes the profile and dynamics of a two-soliton molecule. Using an algebraically-decaying seed solution, we obtain a two-soliton solution with diverging peaks, which we denote as singular soliton molecule. We find that the new solution has a finite binding energy. We calculate the force and potential of interaction between the two solitons, which turn out to be of molecular-type. The robustness of the bond between the two solitons is also verified. Furthermore, we obtain a new solution to the nonlocal NLSE using the same method and seed solution. The new solution in this case corresponds to an elastic collision of a soliton, a breather soliton on flat background, and a breather soliton on a background with linear ramp. Finally, we consider an NLSE which is nonlocal in time rather than space. Although we did not find a Lax pair to this equation, we derive three exact solutions.

arXiv comment7 pages, 5 figures

References in corpus (7)

• Physics with Coherent Matter Waves
• Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
• Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
• Singular solitons
• Antisymmetric solitons and their interactions in strongly dispersion-managed fiber-optic systems
• New classes of solutions in the Coupled PT Symmetric Nonlocal Nonlinear Schrodinger Equations with Four Wave Mixing
• Stability of $N$-soliton molecules in dispersion-managed optical fibers

Cited by in corpus (1)

• Collision of two self-trapped atomic matter wave packets in an optical ring cavity