Sasa-Satsuma equation: soliton on a background and its limiting cases.

We present a multiparameter family of a soliton on a background solution to the Sasa-Satsuma equation. The solution is controlled by a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits a few nontrivial limiting cases that are considered in detail. Among these special cases is the nonlinear Schrödinger equation limit and the limit of rogue wave solutions.

[1]  N. Akhmediev,et al.  Modulation instability and periodic solutions of the nonlinear Schrödinger equation , 1986 .

[2]  Cavalcanti,et al.  Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[3]  Junkichi Satsuma,et al.  New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation , 1991 .

[4]  M. Tabor,et al.  Exact solutions for an extended nonlinear Schrödinger equation , 1991 .

[5]  S. Wabnitz,et al.  Phase detecting of solitons by mixing with a continuous-wave background in an optical fiber , 1992 .

[6]  L. Torner,et al.  Inverse-scattering approach to femtosecond solitons in monomode optical fibers. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  L. Torner,et al.  Soliton solutions for a perturbed nonlinear Schrodinger equation , 1993 .

[8]  D. Mihalache,et al.  The Riemann problem method for solving a perturbed nonlinear Schrodinger equation describing pulse propagation in optic fibres , 1994 .

[9]  Adrian Ankiewicz,et al.  Solitons : nonlinear pulses and beams , 1997 .

[10]  Yosuke Watanabe,et al.  Breather solutions to the focusing nonlinear Schrödinger equation , 1998 .

[11]  M. Trippenbach,et al.  Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media , 1998 .

[12]  J Hietarinta,et al.  Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  A. ADoefaa,et al.  ? ? ? ? f ? ? ? ? ? , 2003 .

[14]  A. Slunyaev.  A high-order nonlinear envelope equation for gravity waves in finite-depth water , 2005 .

[15]  Otis C. Wright,et al.  Sasa-Satsuma Equation, Unstable Plane Waves and Heteroclinic Connections , 2007 .

[16]  N. Akhmediev,et al.  Waves that appear from nowhere and disappear without a trace , 2009 .

[17]  J. Soto-Crespo,et al.  Extreme waves that appear from nowhere: On the nature of rogue waves , 2009 .

[18]  Adrian Ankiewicz,et al.  Rogue waves and rational solutions of the Hirota equation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  B. Wetzel,et al.  Akhmediev breather evolution in optical fiber for realistic initial conditions , 2011 .

[20]  J. Fatome,et al.  Observation of Kuznetsov-Ma soliton dynamics in optical fibre , 2012, Scientific Reports.

[21]  Uwe Bandelow,et al.  Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa-Satsuma case , 2012 .

[22]  Fedor Mitschke,et al.  Possibility of an Akhmediev breather decaying into solitons , 2012 .