Complex and coupled complex negative order AKNS equation

Abstract In this paper, we propose a complex negative order AKNS equation and a coupled complex negative order AKNS equation. They are integrable due to the existence of Lax pairs. Furthermore, we find their multi-soliton solutions in terms of Pfaffians by virtue of Hirota’s bilinear method. One- and two-soliton solutions are investigated in detail exhibiting favorable evolution properties. Especially, the same as the coupled nonlinear Schrodinger equation, inelastic interactions and energy re-distribution happen between two solitons, that has potential applications and deserve further study.

[1]  J. Verosky,et al.  Negative powers of Olver recursion operators , 1991 .

[2]  B. Fuchssteiner.  Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation , 1996 .

[3]  Sergei Sakovich,et al.  The Short Pulse Equation Is Integrable , 2005 .

[4]  Jarmo Hietarinta,et al.  Inelastic Collision and Switching of Coupled Bright Solitons in Optical Fibers , 1997, solv-int/9703008.

[5]  Darryl D. Holm,et al.  A New Integrable Equation with Peakon Solutions , 2002, nlin/0205023.

[6]  Jie Ji,et al.  Soliton scattering with amplitude changes of a negative order AKNS equation , 2009 .

[7]  Chao-Zhong Wu.  On solutions of the two-component Camassa-Holm system , 2006 .

[8]  M Lakshmanan,et al.  Exact soliton solutions of coupled nonlinear Schrödinger equations: shape-changing collisions, logic gates, and partially coherent solitons. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  C. E. Wayne,et al.  Propagation of ultra-short optical pulses in cubic nonlinear media , 2004 .

[10]  Bao-Feng Feng,et al.  Complex short pulse and coupled complex short pulse equations , 2013, 1312.6431.

[11]  Darryl D. Holm,et al.  An integrable shallow water equation with peaked solitons. , 1993, Physical review letters.

[12]  Bao-Feng Feng,et al.  An integrable coupled short pulse equation , 2012 .

[13]  Yoshimasa Matsuno,et al.  A novel multi-component generalization of the short pulse equation and its multisoliton solutions , 2011, 1111.1792.

[14]  M Lakshmanan,et al.  Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations. , 2001, Physical review letters.

[15]  Andrew N.W. Hone,et al.  LETTER TO THE EDITOR: The associated Camassa-Holm equation and the KdV equation , 1999 .

[16]  Youjin Zhang,et al.  A Two-component Generalization of the Camassa-Holm Equation and its Solutions , 2005, nlin/0501028.

[17]  Jianke Yang,et al.  Classification of the solitary waves in coupled nonlinear Schro¨dinger equations , 1997 .

[18]  Uwe Bandelow,et al.  On the propagation of vector ultra-short pulses , 2008 .

[19]  Bao-Feng Feng,et al.  General N-soliton solution to a vector nonlinear Schrödinger equation , 2014 .

[20]  Guo-Fu Yu.  Discrete Analogues of a Negative Order AKNS Equation , 2015 .