Dynamics of various waves in nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity

2020 ◽  
Vol 99 (4) ◽  
pp. 2971-2985
Author(s):  
Cai-qin Song ◽  
Hai-qiong Zhao
Keyword(s):  
Schrödinger Equation ◽  
Raman Scattering ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stimulated Raman Scattering ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Quintic Nonlinearity ◽  
Stimulated Raman

scholarly journals Soliton dynamics in an extended nonlinear Schrödinger equation with a spatial counterpart of the stimulated Raman scattering

2013 ◽  
Vol 79 (6) ◽  
pp. 1057-1062 ◽  
Author(s):  
E. M. GROMOV ◽  
B. A. MALOMED
Keyword(s):  
Schrödinger Equation ◽  
Raman Scattering ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stimulated Raman Scattering ◽  
Low Frequency ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Soliton Dynamics ◽  
Stimulated Raman

AbstractThe dynamics of solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high-frequency (HF) and low-frequency (LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves in plasmas. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (PSRS) term, i.e. a spatial-domain counterpart of the SRS term, which is well known as an ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order diffraction (SOD). It is shown that the wavenumber downshift of solitons, caused by the PSRS, may be compensated by an upshift provided by the SOD whose coefficient is a linear function of the coordinate. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well, including the predicted balance between the PSRS and the linearly inhomogeneous SOD.

scholarly journals Growth of Solutions to NLS on Irrational Tori

2017 ◽  
Vol 2019 (9) ◽  
pp. 2919-2950 ◽  
Author(s):  
Yu Deng ◽  
Pierre Germain
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Strichartz Estimates ◽  
Nonlinear Schrödinger ◽  
Quintic Nonlinearity ◽  
Polynomial Bounds ◽  
Growth Of Solutions

Abstract We prove polynomial bounds on the $H^s$ growth for the nonlinear Schrödinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearity. Due to improved Strichartz estimates, these bounds are better for irrational tori than they are for rational tori.

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