Variational approach to studying solitary waves in the nonlinear Schrödinger equation with complex potentials
[5];
- Univ. of Bayreuth (Germany). Physikalisches Institut
- Santa Fe Inst. (SFI), Santa Fe, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Pontifical Catholic Univ. of Chile, Region Metropolitana (Chile). Dept. de Fisica
- Savitribai Phule Pune Univ., Pune (India)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Here in this paper, we discuss the behavior of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) as they interact with complex potentials, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where the two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope dp(t)/dv(t) becomes negative when plotted parametrically as a function of time, where p(t) is the momentum of the solitary wave and v(t) the velocity.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1414120
- Alternate ID(s):
- OSTI ID: 1324864
- Report Number(s):
- LA-UR-16-23477; TRN: US1800646
- Journal Information:
- Physical Review E, Vol. 94, Issue 3; ISSN 2470-0045
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Exact solutions of a generalized variant of the derivative nonlinear Schrödinger equation in a Scarff II external potential and their stability properties
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journal | October 2018 |
| Exact solutions of a generalized variant of the derivative nonlinear Schrodinger equation in a Scarff II external potential and their stability properties | text | January 2018 |
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