Binary Darboux transformation for the coupled Sasa-Satsuma equations.

The binary Darboux transformation method is applied to the coupled Sasa-Satsuma equations, which can be used to describe the propagation dynamics of femtosecond vector solitons in the birefringent fibers with third-order dispersion, self-steepening, and stimulated Raman scattering higher-order effects. An N-fold iterative formula of the resulting binary Darboux transformation is presented in terms of the quasideterminants. Via the simplest case of this formula, a few of illustrative explicit solutions to the coupled Sasa-Satsuma equations are generated from vanishing and non-vanishing backgrounds, which include the breathers, single- and double-hump bright vector solitons, and anti-dark vector solitons.

[1]  Sudipta Nandy.  Inverse scattering approach to coupled higher-order nonlinear Schrödinger equation and N-soliton solutions , 2004 .

[2]  Danhua Wang,et al.  Soliton and breather solutions of the Sasa–Satsuma equation via the Darboux transformation , 2014 .

[3]  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.

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

[5]  Jm Christian,et al.  Spatiotemporal dark and anti-dark solitons in cubic-quintic photonic systems , 2013 .

[6]  Hai-Qiang Zhang,et al.  Dark and antidark soliton solutions in the modified nonlinear Schrödinger equation with distributed coefficients in inhomogeneous fibers , 2011 .

[7]  M. Soljačić,et al.  Anti-dark spatial solitons with incoherent light , 2000, Quantum Electronics and Laser Science Conference.

[8]  A. Maruta,et al.  Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission , 2002 .

[9]  J. Nimmo,et al.  Binary Darboux transformation for the Sasa–Satsuma equation , 2015, 1502.07371.

[10]  Tao Xu,et al.  Symbolic-computation study of integrable properties for the (2+1)-dimensional Gardner equation with the two-singular-manifold method , 2007, 0707.0787.

[11]  Yuanjiang Xiang,et al.  Observation of anti-dark solitons in fiber lasers , 2016 .

[12]  Yuji Kodama,et al.  Optical solitons in a monomode fiber , 1985 .

[13]  Дж Дж К Ниммо,et al.  Применения преобразований Дарбу к самодуальным уравнениям Янга - Миллса@@@Applications of Darboux transformations to the self-dual Yang - Mills equations , 2000 .

[14]  Soliton Solution, Bäcklund Transformation, and Conservation Laws for the Sasa-Satsuma Equation in the Optical Fiber Communications , 2010 .

[15]  S. Trillo,et al.  Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation , 2011 .

[16]  A. Hasegawa,et al.  Nonlinear pulse propagation in a monomode dielectric guide , 1987 .

[17]  Kenneth Steiglitz,et al.  State transformations of colliding optical solitons and possible application to computation in bulk media , 1998 .

[18]  Tao Xu,et al.  Single- and double-hump femtosecond vector solitons in the coupled Sasa-Satsuma system , 2013 .

[19]  Vinoj,et al.  Multisoliton solutions and integrability aspects of coupled higher-order nonlinear Schrodinger equations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  D. J. Kaup,et al.  Squared Eigenfunctions for the Sasa-Satsuma Equation , 2009, 0902.1210.

[21]  Porsezian,et al.  Coupled higher-order nonlinear Schrödinger equations in nonlinear optics: Painlevé analysis and integrability. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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